LMFDB - Embedded newform 15.3.f.a.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,3,Mod(7,15)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("15.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	15.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.408720396540$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.2
Root			$1.22474 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	15.7
Dual form			15.3.f.a.13.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.224745 + 0.224745i) q^{2} +(-1.22474 + 1.22474i) q^{3} -3.89898i q^{4} +(-4.67423 + 1.77526i) q^{5} -0.550510 q^{6} +(3.44949 + 3.44949i) q^{7} +(1.77526 - 1.77526i) q^{8} -3.00000i q^{9} +(-1.44949 - 0.651531i) q^{10} +11.3485 q^{11} +(4.77526 + 4.77526i) q^{12} +(-5.55051 + 5.55051i) q^{13} +1.55051i q^{14} +(3.55051 - 7.89898i) q^{15} -14.7980 q^{16} +(-17.3485 - 17.3485i) q^{17} +(0.674235 - 0.674235i) q^{18} +8.69694i q^{19} +(6.92168 + 18.2247i) q^{20} -8.44949 q^{21} +(2.55051 + 2.55051i) q^{22} +(11.5505 - 11.5505i) q^{23} +4.34847i q^{24} +(18.6969 - 16.5959i) q^{25} -2.49490 q^{26} +(3.67423 + 3.67423i) q^{27} +(13.4495 - 13.4495i) q^{28} +35.1464i q^{29} +(2.57321 - 0.977296i) q^{30} +10.6969 q^{31} +(-10.4268 - 10.4268i) q^{32} +(-13.8990 + 13.8990i) q^{33} -7.79796i q^{34} +(-22.2474 - 10.0000i) q^{35} -11.6969 q^{36} +(-6.04541 - 6.04541i) q^{37} +(-1.95459 + 1.95459i) q^{38} -13.5959i q^{39} +(-5.14643 + 11.4495i) q^{40} +0.696938 q^{41} +(-1.89898 - 1.89898i) q^{42} +(-26.4949 + 26.4949i) q^{43} -44.2474i q^{44} +(5.32577 + 14.0227i) q^{45} +5.19184 q^{46} +(44.2474 + 44.2474i) q^{47} +(18.1237 - 18.1237i) q^{48} -25.2020i q^{49} +(7.93189 + 0.472194i) q^{50} +42.4949 q^{51} +(21.6413 + 21.6413i) q^{52} +(-0.696938 + 0.696938i) q^{53} +1.65153i q^{54} +(-53.0454 + 20.1464i) q^{55} +12.2474 q^{56} +(-10.6515 - 10.6515i) q^{57} +(-7.89898 + 7.89898i) q^{58} -39.9342i q^{59} +(-30.7980 - 13.8434i) q^{60} +5.90918 q^{61} +(2.40408 + 2.40408i) q^{62} +(10.3485 - 10.3485i) q^{63} +54.5051i q^{64} +(16.0908 - 35.7980i) q^{65} -6.24745 q^{66} +(-45.1010 - 45.1010i) q^{67} +(-67.6413 + 67.6413i) q^{68} +28.2929i q^{69} +(-2.75255 - 7.24745i) q^{70} -68.0000 q^{71} +(-5.32577 - 5.32577i) q^{72} +(77.7878 - 77.7878i) q^{73} -2.71735i q^{74} +(-2.57321 + 43.2247i) q^{75} +33.9092 q^{76} +(39.1464 + 39.1464i) q^{77} +(3.05561 - 3.05561i) q^{78} -24.4949i q^{79} +(69.1691 - 26.2702i) q^{80} -9.00000 q^{81} +(0.156633 + 0.156633i) q^{82} +(13.1464 - 13.1464i) q^{83} +32.9444i q^{84} +(111.889 + 50.2929i) q^{85} -11.9092 q^{86} +(-43.0454 - 43.0454i) q^{87} +(20.1464 - 20.1464i) q^{88} +82.1816i q^{89} +(-1.95459 + 4.34847i) q^{90} -38.2929 q^{91} +(-45.0352 - 45.0352i) q^{92} +(-13.1010 + 13.1010i) q^{93} +19.8888i q^{94} +(-15.4393 - 40.6515i) q^{95} +25.5403 q^{96} +(-24.5959 - 24.5959i) q^{97} +(5.66403 - 5.66403i) q^{98} -34.0454i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 4 q^{5} - 12 q^{6} + 4 q^{7} + 12 q^{8} + 4 q^{10} + 16 q^{11} + 24 q^{12} - 32 q^{13} + 24 q^{15} - 20 q^{16} - 40 q^{17} - 12 q^{18} - 36 q^{20} - 24 q^{21} + 20 q^{22} + 56 q^{23} + 16 q^{25}+ \cdots - 188 q^{98}+O(q^{100}) $ 4 * q - 4 * q^2 - 4 * q^5 - 12 * q^6 + 4 * q^7 + 12 * q^8 + 4 * q^10 + 16 * q^11 + 24 * q^12 - 32 * q^13 + 24 * q^15 - 20 * q^16 - 40 * q^17 - 12 * q^18 - 36 * q^20 - 24 * q^21 + 20 * q^22 + 56 * q^23 + 16 * q^25 + 88 * q^26 + 44 * q^28 - 24 * q^30 - 16 * q^31 - 76 * q^32 - 36 * q^33 - 40 * q^35 + 12 * q^36 + 64 * q^37 - 96 * q^38 + 48 * q^40 - 56 * q^41 + 12 * q^42 - 8 * q^43 + 36 * q^45 - 136 * q^46 + 128 * q^47 + 48 * q^48 + 164 * q^50 + 72 * q^51 - 80 * q^52 + 56 * q^53 - 124 * q^55 - 72 * q^57 - 12 * q^58 - 84 * q^60 + 200 * q^61 + 88 * q^62 + 12 * q^63 - 112 * q^65 + 24 * q^66 - 200 * q^67 - 104 * q^68 - 60 * q^70 - 272 * q^71 - 36 * q^72 + 76 * q^73 + 24 * q^75 + 312 * q^76 + 88 * q^77 + 120 * q^78 + 164 * q^80 - 36 * q^81 + 128 * q^82 - 16 * q^83 + 232 * q^85 - 224 * q^86 - 84 * q^87 + 12 * q^88 - 96 * q^90 - 16 * q^91 + 104 * q^92 - 72 * q^93 + 144 * q^95 - 84 * q^96 - 20 * q^97 - 188 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/15\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.224745	+	0.224745i	0.112372	+	0.112372i	0.761057	−	0.648685i	$-0.224681\pi$
$2$	0.224745	+	0.224745i	0.112372	+	0.112372i	−0.648685	+	0.761057i	$0.724681\pi$
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$4$		−	3.89898i		−	0.974745i
$5$	−4.67423	+	1.77526i	−0.934847	+	0.355051i
$5$	−4.67423	+	1.77526i	−0.934847	+	0.355051i
$6$	−0.550510			−0.0917517
$7$	3.44949	+	3.44949i	0.492784	+	0.492784i	0.909182	−	0.416398i	$-0.136708\pi$
$7$	3.44949	+	3.44949i	0.492784	+	0.492784i	−0.416398	+	0.909182i	$0.636708\pi$
$8$	1.77526	−	1.77526i	0.221907	−	0.221907i
$9$		−	3.00000i		−	0.333333i
$10$	−1.44949	−	0.651531i	−0.144949	−	0.0651531i
$11$	11.3485			1.03168			0.515840	−	0.856685i	$-0.327480\pi$
$11$	11.3485			1.03168			0.515840	+	0.856685i	$0.327480\pi$
$12$	4.77526	+	4.77526i	0.397938	+	0.397938i
$13$	−5.55051	+	5.55051i	−0.426962	+	0.426962i	−0.887592	−	0.460630i	$-0.847624\pi$
$13$	−5.55051	+	5.55051i	−0.426962	+	0.426962i	0.460630	+	0.887592i	$0.347624\pi$
$14$			1.55051i			0.110751i
$15$	3.55051	−	7.89898i	0.236701	−	0.526599i
$16$	−14.7980			−0.924872
$17$	−17.3485	−	17.3485i	−1.02050	−	1.02050i	−0.999785	−	0.0207127i	$-0.993406\pi$
$17$	−17.3485	−	17.3485i	−1.02050	−	1.02050i	−0.0207127	−	0.999785i	$-0.506594\pi$
$18$	0.674235	−	0.674235i	0.0374575	−	0.0374575i
$19$			8.69694i			0.457734i	0.973458	+	0.228867i	$0.0735020\pi$
$19$			8.69694i			0.457734i	−0.973458	+	0.228867i	$0.926498\pi$
$20$	6.92168	+	18.2247i	0.346084	+	0.911237i
$21$	−8.44949			−0.402357
$22$	2.55051	+	2.55051i	0.115932	+	0.115932i
$23$	11.5505	−	11.5505i	0.502196	−	0.502196i	−0.409924	−	0.912120i	$-0.634445\pi$
$23$	11.5505	−	11.5505i	0.502196	−	0.502196i	0.912120	+	0.409924i	$0.134445\pi$
$24$			4.34847i			0.181186i
$25$	18.6969	−	16.5959i	0.747878	−	0.663837i
$26$	−2.49490			−0.0959576
$27$	3.67423	+	3.67423i	0.136083	+	0.136083i
$28$	13.4495	−	13.4495i	0.480339	−	0.480339i
$29$			35.1464i			1.21195i	0.795485	+	0.605973i	$0.207216\pi$
$29$			35.1464i			1.21195i	−0.795485	+	0.605973i	$0.792784\pi$
$30$	2.57321	−	0.977296i	0.0857738	−	0.0325765i
$31$	10.6969			0.345063			0.172531	−	0.985004i	$-0.444805\pi$
$31$	10.6969			0.345063			0.172531	+	0.985004i	$0.444805\pi$
$32$	−10.4268	−	10.4268i	−0.325837	−	0.325837i
$33$	−13.8990	+	13.8990i	−0.421181	+	0.421181i
$34$		−	7.79796i		−	0.229352i
$35$	−22.2474	−	10.0000i	−0.635641	−	0.285714i
$36$	−11.6969			−0.324915
$37$	−6.04541	−	6.04541i	−0.163389	−	0.163389i	0.620677	−	0.784066i	$-0.286858\pi$
$37$	−6.04541	−	6.04541i	−0.163389	−	0.163389i	−0.784066	+	0.620677i	$0.786858\pi$
$38$	−1.95459	+	1.95459i	−0.0514366	+	0.0514366i
$39$		−	13.5959i		−	0.348613i
$40$	−5.14643	+	11.4495i	−0.128661	+	0.286237i
$41$	0.696938			0.0169985			0.00849925	−	0.999964i	$-0.497295\pi$
$41$	0.696938			0.0169985			0.00849925	+	0.999964i	$0.497295\pi$
$42$	−1.89898	−	1.89898i	−0.0452138	−	0.0452138i
$43$	−26.4949	+	26.4949i	−0.616160	+	0.616160i	−0.944544	−	0.328384i	$-0.893496\pi$
$43$	−26.4949	+	26.4949i	−0.616160	+	0.616160i	0.328384	+	0.944544i	$0.393496\pi$
$44$		−	44.2474i		−	1.00562i
$45$	5.32577	+	14.0227i	0.118350	+	0.311616i
$46$	5.19184			0.112866
$47$	44.2474	+	44.2474i	0.941435	+	0.941435i	0.998377	−	0.0569424i	$-0.0181351\pi$
$47$	44.2474	+	44.2474i	0.941435	+	0.941435i	−0.0569424	+	0.998377i	$0.518135\pi$
$48$	18.1237	−	18.1237i	0.377578	−	0.377578i
$49$		−	25.2020i		−	0.514327i
$50$	7.93189	+	0.472194i	0.158638	+	0.00944387i
$51$	42.4949			0.833233
$52$	21.6413	+	21.6413i	0.416179	+	0.416179i
$53$	−0.696938	+	0.696938i	−0.0131498	+	0.0131498i	−0.713651	−	0.700501i	$-0.752960\pi$
$53$	−0.696938	+	0.696938i	−0.0131498	+	0.0131498i	0.700501	+	0.713651i	$0.252960\pi$
$54$			1.65153i			0.0305839i
$55$	−53.0454	+	20.1464i	−0.964462	+	0.366299i
$56$	12.2474			0.218704
$57$	−10.6515	−	10.6515i	−0.186869	−	0.186869i
$58$	−7.89898	+	7.89898i	−0.136189	+	0.136189i
$59$		−	39.9342i		−	0.676851i	−0.940993	−	0.338425i	$-0.890106\pi$
$59$		−	39.9342i		−	0.676851i	0.940993	−	0.338425i	$-0.109894\pi$
$60$	−30.7980	−	13.8434i	−0.513299	−	0.230723i
$61$	5.90918			0.0968719			0.0484359	−	0.998826i	$-0.484576\pi$
$61$	5.90918			0.0968719			0.0484359	+	0.998826i	$0.484576\pi$
$62$	2.40408	+	2.40408i	0.0387755	+	0.0387755i
$63$	10.3485	−	10.3485i	0.164261	−	0.164261i
$64$			54.5051i			0.851642i
$65$	16.0908	−	35.7980i	0.247551	−	0.550738i
$66$	−6.24745			−0.0946583
$67$	−45.1010	−	45.1010i	−0.673150	−	0.673150i	0.285291	−	0.958441i	$-0.407910\pi$
$67$	−45.1010	−	45.1010i	−0.673150	−	0.673150i	−0.958441	+	0.285291i	$0.907910\pi$
$68$	−67.6413	+	67.6413i	−0.994725	+	0.994725i
$69$			28.2929i			0.410041i
$70$	−2.75255	−	7.24745i	−0.0393222	−	0.103535i
$71$	−68.0000			−0.957746			−0.478873	−	0.877884i	$-0.658955\pi$
$71$	−68.0000			−0.957746			−0.478873	+	0.877884i	$0.658955\pi$
$72$	−5.32577	−	5.32577i	−0.0739690	−	0.0739690i
$73$	77.7878	−	77.7878i	1.06559	−	1.06559i	0.0678931	−	0.997693i	$-0.478372\pi$
$73$	77.7878	−	77.7878i	1.06559	−	1.06559i	0.997693	−	0.0678931i	$-0.0216277\pi$
$74$		−	2.71735i		−	0.0367209i
$75$	−2.57321	+	43.2247i	−0.0343095	+	0.576330i
$76$	33.9092			0.446173
$77$	39.1464	+	39.1464i	0.508395	+	0.508395i
$78$	3.05561	−	3.05561i	0.0391745	−	0.0391745i
$79$		−	24.4949i		−	0.310062i	−0.987910	−	0.155031i	$-0.950452\pi$
$79$		−	24.4949i		−	0.310062i	0.987910	−	0.155031i	$-0.0495477\pi$
$80$	69.1691	−	26.2702i	0.864614	−	0.328377i
$81$	−9.00000			−0.111111
$82$	0.156633	+	0.156633i	0.00191016	+	0.00191016i
$83$	13.1464	−	13.1464i	0.158391	−	0.158391i	−0.623463	−	0.781853i	$-0.714275\pi$
$83$	13.1464	−	13.1464i	0.158391	−	0.158391i	0.781853	+	0.623463i	$0.214275\pi$
$84$			32.9444i			0.392195i
$85$	111.889	+	50.2929i	1.31634	+	0.591681i
$86$	−11.9092			−0.138479
$87$	−43.0454	−	43.0454i	−0.494775	−	0.494775i
$88$	20.1464	−	20.1464i	0.228937	−	0.228937i
$89$			82.1816i			0.923389i	0.887039	+	0.461695i	$0.152758\pi$
$89$			82.1816i			0.923389i	−0.887039	+	0.461695i	$0.847242\pi$
$90$	−1.95459	+	4.34847i	−0.0217177	+	0.0483163i
$91$	−38.2929			−0.420801
$92$	−45.0352	−	45.0352i	−0.489513	−	0.489513i
$93$	−13.1010	+	13.1010i	−0.140871	+	0.140871i
$94$			19.8888i			0.211583i
$95$	−15.4393	−	40.6515i	−0.162519	−	0.427911i
$96$	25.5403			0.266045
$97$	−24.5959	−	24.5959i	−0.253566	−	0.253566i	0.568865	−	0.822431i	$-0.307383\pi$
$97$	−24.5959	−	24.5959i	−0.253566	−	0.253566i	−0.822431	+	0.568865i	$0.807383\pi$
$98$	5.66403	−	5.66403i	0.0577962	−	0.0577962i
$99$		−	34.0454i		−	0.343893i
$100$	−64.7071	−	72.8990i	−0.647071	−	0.728990i
$101$	−105.621			−1.04575			−0.522876	−	0.852409i	$-0.675141\pi$
$101$	−105.621			−1.04575			−0.522876	+	0.852409i	$0.675141\pi$
$102$	9.55051	+	9.55051i	0.0936325	+	0.0936325i
$103$	−89.2474	+	89.2474i	−0.866480	+	0.866480i	−0.992081	−	0.125601i	$-0.959914\pi$
$103$	−89.2474	+	89.2474i	−0.866480	+	0.866480i	0.125601	+	0.992081i	$0.459914\pi$
$104$			19.7071i			0.189492i
$105$	39.4949	−	15.0000i	0.376142	−	0.142857i
$106$	−0.313267			−0.00295535
$107$	68.7423	+	68.7423i	0.642452	+	0.642452i	0.951158	−	0.308706i	$-0.0998958\pi$
$107$	68.7423	+	68.7423i	0.642452	+	0.642452i	−0.308706	+	0.951158i	$0.599896\pi$
$108$	14.3258	−	14.3258i	0.132646	−	0.132646i
$109$			68.6969i			0.630247i	0.949051	+	0.315124i	$0.102046\pi$
$109$			68.6969i			0.630247i	−0.949051	+	0.315124i	$0.897954\pi$
$110$	−16.4495	−	7.39388i	−0.149541	−	0.0672171i
$111$	14.8082			0.133407
$112$	−51.0454	−	51.0454i	−0.455763	−	0.455763i
$113$	97.6413	−	97.6413i	0.864083	−	0.864083i	−0.127727	−	0.991809i	$-0.540768\pi$
$113$	97.6413	−	97.6413i	0.864083	−	0.864083i	0.991809	+	0.127727i	$0.0407681\pi$
$114$		−	4.78775i		−	0.0419978i
$115$	−33.4847	+	74.4949i	−0.291171	+	0.647782i
$116$	137.035			1.18134
$117$	16.6515	+	16.6515i	0.142321	+	0.142321i
$118$	8.97500	−	8.97500i	0.0760593	−	0.0760593i
$119$		−	119.687i		−	1.00577i
$120$	−7.71964	−	20.3258i	−0.0643304	−	0.169381i
$121$	7.78775			0.0643616
$122$	1.32806	+	1.32806i	0.0108857	+	0.0108857i
$123$	−0.853572	+	0.853572i	−0.00693961	+	0.00693961i
$124$		−	41.7071i		−	0.336348i
$125$	−57.9319	+	110.765i	−0.463455	+	0.886120i
$126$	4.65153			0.0369169
$127$	164.621	+	164.621i	1.29623	+	1.29623i	0.930865	+	0.365362i	$0.119055\pi$
$127$	164.621	+	164.621i	1.29623	+	1.29623i	0.365362	+	0.930865i	$0.380945\pi$
$128$	−53.9569	+	53.9569i	−0.421538	+	0.421538i
$129$		−	64.8990i		−	0.503093i
$130$	11.6617	−	4.42908i	0.0897057	−	0.0340698i
$131$	106.136			0.810200			0.405100	−	0.914272i	$-0.367237\pi$
$131$	106.136			0.810200			0.405100	+	0.914272i	$0.367237\pi$
$132$	54.1918	+	54.1918i	0.410544	+	0.410544i
$133$	−30.0000	+	30.0000i	−0.225564	+	0.225564i
$134$		−	20.2724i		−	0.151287i
$135$	−23.6969	−	10.6515i	−0.175533	−	0.0789002i
$136$	−61.5959			−0.452911
$137$	−166.631	−	166.631i	−1.21629	−	1.21629i	−0.968923	−	0.247363i	$-0.920436\pi$
$137$	−166.631	−	166.631i	−1.21629	−	1.21629i	−0.247363	−	0.968923i	$-0.579564\pi$
$138$	−6.35867	+	6.35867i	−0.0460774	+	0.0460774i
$139$		−	191.171i		−	1.37533i	−0.726026	−	0.687667i	$-0.758635\pi$
$139$		−	191.171i		−	1.37533i	0.726026	−	0.687667i	$-0.241365\pi$
$140$	−38.9898	+	86.7423i	−0.278499	+	0.619588i
$141$	−108.384			−0.768679
$142$	−15.2827	−	15.2827i	−0.107624	−	0.107624i
$143$	−62.9898	+	62.9898i	−0.440488	+	0.440488i
$144$			44.3939i			0.308291i
$145$	−62.3939	−	164.283i	−0.430303	−	1.13298i
$146$	34.9648			0.239485
$147$	30.8661	+	30.8661i	0.209973	+	0.209973i
$148$	−23.5709	+	23.5709i	−0.159263	+	0.159263i
$149$			84.8536i			0.569487i	0.958604	+	0.284744i	$0.0919084\pi$
$149$			84.8536i			0.569487i	−0.958604	+	0.284744i	$0.908092\pi$
$150$	−10.2929	+	9.13622i	−0.0686190	+	0.0609082i
$151$	148.969			0.986552			0.493276	−	0.869873i	$-0.335799\pi$
$151$	148.969			0.986552			0.493276	+	0.869873i	$0.335799\pi$
$152$	15.4393	+	15.4393i	0.101574	+	0.101574i
$153$	−52.0454	+	52.0454i	−0.340166	+	0.340166i
$154$			17.5959i			0.114259i
$155$	−50.0000	+	18.9898i	−0.322581	+	0.122515i
$156$	−53.0102			−0.339809
$157$	16.8536	+	16.8536i	0.107348	+	0.107348i	0.758741	−	0.651393i	$-0.225815\pi$
$157$	16.8536	+	16.8536i	0.107348	+	0.107348i	−0.651393	+	0.758741i	$0.725815\pi$
$158$	5.50510	−	5.50510i	0.0348424	−	0.0348424i
$159$		−	1.70714i		−	0.0107368i
$160$	67.2474	+	30.2270i	0.420297	+	0.188919i
$161$	79.6867			0.494949
$162$	−2.02270	−	2.02270i	−0.0124858	−	0.0124858i
$163$	130.606	−	130.606i	0.801265	−	0.801265i	−0.182029	−	0.983293i	$-0.558266\pi$
$163$	130.606	−	130.606i	0.801265	−	0.801265i	0.983293	+	0.182029i	$0.0582664\pi$
$164$		−	2.71735i		−	0.0165692i
$165$	40.2929	−	89.6413i	0.244199	−	0.543281i
$166$	5.90918			0.0355975
$167$	−45.0352	−	45.0352i	−0.269672	−	0.269672i	0.559296	−	0.828968i	$-0.311071\pi$
$167$	−45.0352	−	45.0352i	−0.269672	−	0.269672i	−0.828968	+	0.559296i	$0.811071\pi$
$168$	−15.0000	+	15.0000i	−0.0892857	+	0.0892857i
$169$			107.384i			0.635406i
$170$	13.8434	+	36.4495i	0.0814316	+	0.214409i
$171$	26.0908			0.152578
$172$	103.303	+	103.303i	0.600599	+	0.600599i
$173$	146.631	−	146.631i	0.847579	−	0.847579i	−0.142252	−	0.989831i	$-0.545434\pi$
$173$	146.631	−	146.631i	0.847579	−	0.847579i	0.989831	+	0.142252i	$0.0454343\pi$
$174$		−	19.3485i		−	0.111198i
$175$	121.742	+	7.24745i	0.695671	+	0.0414140i
$176$	−167.934			−0.954171
$177$	48.9092	+	48.9092i	0.276323	+	0.276323i
$178$	−18.4699	+	18.4699i	−0.103763	+	0.103763i
$179$			183.712i			1.02632i	0.858292	+	0.513161i	$0.171526\pi$
$179$			183.712i			1.02632i	−0.858292	+	0.513161i	$0.828474\pi$
$180$	54.6742	−	20.7650i	0.303746	−	0.115361i
$181$	−286.272			−1.58162			−0.790808	−	0.612064i	$-0.790339\pi$
$181$	−286.272			−1.58162			−0.790808	+	0.612064i	$0.790339\pi$
$182$	−8.60612	−	8.60612i	−0.0472864	−	0.0472864i
$183$	−7.23724	+	7.23724i	−0.0395478	+	0.0395478i
$184$		−	41.0102i		−	0.222882i
$185$	38.9898	+	17.5255i	0.210756	+	0.0947325i
$186$	−5.88877			−0.0316601
$187$	−196.879	−	196.879i	−1.05283	−	1.05283i
$188$	172.520	−	172.520i	0.917659	−	0.917659i
$189$			25.3485i			0.134119i
$190$	5.66632	−	12.6061i	0.0298228	−	0.0663480i
$191$	48.0908			0.251784			0.125892	−	0.992044i	$-0.459821\pi$
$191$	48.0908			0.251784			0.125892	+	0.992044i	$0.459821\pi$
$192$	−66.7548	−	66.7548i	−0.347681	−	0.347681i
$193$	−255.565	+	255.565i	−1.32417	+	1.32417i	−0.413809	+	0.910364i	$0.635802\pi$
$193$	−255.565	+	255.565i	−1.32417	+	1.32417i	−0.910364	+	0.413809i	$0.864198\pi$
$194$		−	11.0556i		−	0.0569877i
$195$	24.1362	+	63.5505i	0.123776	+	0.325900i
$196$	−98.2622			−0.501338
$197$	−96.6969	−	96.6969i	−0.490847	−	0.490847i	0.417726	−	0.908573i	$-0.362827\pi$
$197$	−96.6969	−	96.6969i	−0.490847	−	0.490847i	−0.908573	+	0.417726i	$0.862827\pi$
$198$	7.65153	−	7.65153i	0.0386441	−	0.0386441i
$199$			192.606i			0.967870i	0.875104	+	0.483935i	$0.160793\pi$
$199$			192.606i			0.967870i	−0.875104	+	0.483935i	$0.839207\pi$
$200$	3.72985	−	62.6538i	0.0186492	−	0.313269i
$201$	110.474			0.549624
$202$	−23.7378	−	23.7378i	−0.117514	−	0.117514i
$203$	−121.237	+	121.237i	−0.597228	+	0.597228i
$204$		−	165.687i		−	0.812190i
$205$	−3.25765	+	1.23724i	−0.0158910	+	0.00603533i
$206$	−40.1158			−0.194737
$207$	−34.6515	−	34.6515i	−0.167399	−	0.167399i
$208$	82.1362	−	82.1362i	0.394886	−	0.394886i
$209$			98.6969i			0.472234i
$210$	12.2474	+	5.50510i	0.0583212	+	0.0262148i
$211$	147.212			0.697688			0.348844	−	0.937181i	$-0.386574\pi$
$211$	147.212			0.697688			0.348844	+	0.937181i	$0.386574\pi$
$212$	2.71735	+	2.71735i	0.0128177	+	0.0128177i
$213$	83.2827	−	83.2827i	0.390998	−	0.390998i
$214$			30.8990i			0.144388i
$215$	76.8082	−	170.879i	0.357247	−	0.794784i
$216$	13.0454			0.0603954
$217$	36.8990	+	36.8990i	0.170041	+	0.170041i
$218$	−15.4393	+	15.4393i	−0.0708224	+	0.0708224i
$219$			190.540i			0.870047i
$220$	78.5505	+	206.823i	0.357048	+	0.940104i
$221$	192.586			0.871429
$222$	3.32806	+	3.32806i	0.0149913	+	0.0149913i
$223$	167.429	−	167.429i	0.750803	−	0.750803i	−0.223826	−	0.974629i	$-0.571855\pi$
$223$	167.429	−	167.429i	0.750803	−	0.750803i	0.974629	+	0.223826i	$0.0718548\pi$
$224$		−	71.9342i		−	0.321135i
$225$	−49.7878	−	56.0908i	−0.221279	−	0.249293i
$226$	43.8888			0.194198
$227$	253.171	+	253.171i	1.11529	+	1.11529i	0.992423	+	0.122870i	$0.0392098\pi$
$227$	253.171	+	253.171i	1.11529	+	1.11529i	0.122870	+	0.992423i	$0.460790\pi$
$228$	−41.5301	+	41.5301i	−0.182150	+	0.182150i
$229$		−	224.202i		−	0.979048i	−0.871990	−	0.489524i	$-0.837171\pi$
$229$		−	224.202i		−	0.979048i	0.871990	−	0.489524i	$-0.162829\pi$
$230$	−24.2679	+	9.21683i	−0.105512	+	0.0400732i
$231$	−95.8888			−0.415103
$232$	62.3939	+	62.3939i	0.268939	+	0.268939i
$233$	−205.712	+	205.712i	−0.882883	+	0.882883i	−0.993827	−	0.110944i	$-0.964613\pi$
$233$	−205.712	+	205.712i	−0.882883	+	0.882883i	0.110944	+	0.993827i	$0.464613\pi$
$234$			7.48469i			0.0319859i
$235$	−285.373	−	128.272i	−1.21436	−	0.545840i
$236$	−155.703			−0.659757
$237$	30.0000	+	30.0000i	0.126582	+	0.126582i
$238$	26.8990	−	26.8990i	0.113021	−	0.113021i
$239$		−	345.798i		−	1.44685i	−0.690401	−	0.723427i	$-0.742566\pi$
$239$		−	345.798i		−	1.44685i	0.690401	−	0.723427i	$-0.257434\pi$
$240$	−52.5403	+	116.889i	−0.218918	+	0.487037i
$241$	101.576			0.421475			0.210738	−	0.977543i	$-0.432413\pi$
$241$	101.576			0.421475			0.210738	+	0.977543i	$0.432413\pi$
$242$	1.75026	+	1.75026i	0.00723247	+	0.00723247i
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$		−	23.0398i		−	0.0944254i
$245$	44.7401	+	117.800i	0.182612	+	0.480817i
$246$	−0.383672			−0.00155964
$247$	−48.2724	−	48.2724i	−0.195435	−	0.195435i
$248$	18.9898	−	18.9898i	0.0765718	−	0.0765718i
$249$			32.2020i			0.129325i
$250$	−37.9138	+	11.8740i	−0.151655	+	0.0474959i
$251$	−331.258			−1.31975			−0.659876	−	0.751375i	$-0.729391\pi$
$251$	−331.258			−1.31975			−0.659876	+	0.751375i	$0.729391\pi$
$252$	−40.3485	−	40.3485i	−0.160113	−	0.160113i
$253$	131.081	−	131.081i	0.518105	−	0.518105i
$254$			73.9954i			0.291321i
$255$	−198.631	+	75.4393i	−0.778946	+	0.295840i
$256$	193.767			0.756904
$257$	33.2372	+	33.2372i	0.129328	+	0.129328i	0.768808	−	0.639480i	$-0.220850\pi$
$257$	33.2372	+	33.2372i	0.129328	+	0.129328i	−0.639480	+	0.768808i	$0.720850\pi$
$258$	14.5857	−	14.5857i	0.0565338	−	0.0565338i
$259$		−	41.7071i		−	0.161031i
$260$	−139.576	−	62.7378i	−0.536829	−	0.241299i
$261$	105.439			0.403982
$262$	23.8536	+	23.8536i	0.0910442	+	0.0910442i
$263$	−278.157	+	278.157i	−1.05763	+	1.05763i	−0.0593952	+	0.998235i	$0.518917\pi$
$263$	−278.157	+	278.157i	−1.05763	+	1.05763i	−0.998235	+	0.0593952i	$0.981083\pi$
$264$			49.3485i			0.186926i
$265$	2.02041	−	4.49490i	0.00762419	−	0.0169619i
$266$	−13.4847			−0.0506943
$267$	−100.652	−	100.652i	−0.376972	−	0.376972i
$268$	−175.848	+	175.848i	−0.656149	+	0.656149i
$269$		−	488.499i		−	1.81598i	−0.418988	−	0.907992i	$-0.637615\pi$
$269$		−	488.499i		−	1.81598i	0.418988	−	0.907992i	$-0.362385\pi$
$270$	−2.93189	−	7.71964i	−0.0108588	−	0.0285913i
$271$	131.576			0.485518			0.242759	−	0.970087i	$-0.421947\pi$
$271$	131.576			0.485518			0.242759	+	0.970087i	$0.421947\pi$
$272$	256.722	+	256.722i	0.943831	+	0.943831i
$273$	46.8990	−	46.8990i	0.171791	−	0.171791i
$274$		−	74.8990i		−	0.273354i
$275$	212.182	−	188.338i	0.771570	−	0.684866i
$276$	110.313			0.399686
$277$	101.510	+	101.510i	0.366461	+	0.366461i	0.866185	−	0.499724i	$-0.166565\pi$
$277$	101.510	+	101.510i	0.366461	+	0.366461i	−0.499724	+	0.866185i	$0.666565\pi$
$278$	42.9648	−	42.9648i	0.154550	−	0.154550i
$279$		−	32.0908i		−	0.115021i
$280$	−57.2474	+	21.7423i	−0.204455	+	0.0776512i
$281$	343.303			1.22172			0.610860	−	0.791739i	$-0.290824\pi$
$281$	343.303			1.22172			0.610860	+	0.791739i	$0.290824\pi$
$282$	−24.3587	−	24.3587i	−0.0863783	−	0.0863783i
$283$	1.19184	−	1.19184i	0.00421143	−	0.00421143i	−0.704998	−	0.709209i	$-0.749052\pi$
$283$	1.19184	−	1.19184i	0.00421143	−	0.00421143i	0.709209	+	0.704998i	$0.249052\pi$
$284$			265.131i			0.933558i
$285$	68.6969	+	30.8786i	0.241042	+	0.108346i
$286$	−28.3133			−0.0989974
$287$	2.40408	+	2.40408i	0.00837659	+	0.00837659i
$288$	−31.2804	+	31.2804i	−0.108612	+	0.108612i
$289$			312.939i			1.08283i
$290$	22.8990	−	50.9444i	0.0789620	−	0.175670i
$291$	60.2474			0.207036
$292$	−303.293	−	303.293i	−1.03867	−	1.03867i
$293$	96.5653	−	96.5653i	0.329574	−	0.329574i	−0.522850	−	0.852425i	$-0.675131\pi$
$293$	96.5653	−	96.5653i	0.329574	−	0.329574i	0.852425	+	0.522850i	$0.175131\pi$
$294$			13.8740i			0.0471904i
$295$	70.8934	+	186.662i	0.240316	+	0.632752i
$296$	−21.4643			−0.0725145
$297$	41.6969	+	41.6969i	0.140394	+	0.140394i
$298$	−19.0704	+	19.0704i	−0.0639946	+	0.0639946i
$299$			128.222i			0.428838i
$300$	168.532	+	10.0329i	0.561775	+	0.0334430i
$301$	−182.788			−0.607268
$302$	33.4801	+	33.4801i	0.110861	+	0.110861i
$303$	129.359	−	129.359i	0.426926	−	0.426926i
$304$		−	128.697i		−	0.423345i
$305$	−27.6209	+	10.4903i	−0.0905604	+	0.0343945i
$306$	−23.3939			−0.0764506
$307$	−124.969	−	124.969i	−0.407066	−	0.407066i	0.473648	−	0.880714i	$-0.342937\pi$
$307$	−124.969	−	124.969i	−0.407066	−	0.407066i	−0.880714	+	0.473648i	$0.842937\pi$
$308$	152.631	−	152.631i	0.495556	−	0.495556i
$309$		−	218.611i		−	0.707478i
$310$	−15.5051	−	6.96938i	−0.0500165	−	0.0224819i
$311$	−586.302			−1.88522			−0.942608	−	0.333902i	$-0.891635\pi$
$311$	−586.302			−1.88522			−0.942608	+	0.333902i	$0.891635\pi$
$312$	−24.1362	−	24.1362i	−0.0773597	−	0.0773597i
$313$	−102.373	+	102.373i	−0.327072	+	0.327072i	−0.851472	−	0.524400i	$-0.824290\pi$
$313$	−102.373	+	102.373i	−0.327072	+	0.327072i	0.524400	+	0.851472i	$0.324290\pi$
$314$			7.57551i			0.0241258i
$315$	−30.0000	+	66.7423i	−0.0952381	+	0.211880i
$316$	−95.5051			−0.302231
$317$	−108.783	−	108.783i	−0.343165	−	0.343165i	0.514391	−	0.857556i	$-0.328018\pi$
$317$	−108.783	−	108.783i	−0.343165	−	0.343165i	−0.857556	+	0.514391i	$0.828018\pi$
$318$	0.383672	−	0.383672i	0.00120651	−	0.00120651i
$319$			398.858i			1.25034i
$320$	−96.7605	−	254.770i	−0.302376	−	0.796155i
$321$	−168.384			−0.524560
$322$	17.9092	+	17.9092i	0.0556186	+	0.0556186i
$323$	150.879	−	150.879i	0.467116	−	0.467116i
$324$			35.0908i			0.108305i
$325$	−11.6617	+	195.893i	−0.0358823	+	0.602749i
$326$	58.7061			0.180080
$327$	−84.1362	−	84.1362i	−0.257297	−	0.257297i
$328$	1.23724	−	1.23724i	0.00377208	−	0.00377208i
$329$			305.262i			0.927849i
$330$	29.2020	−	11.0908i	0.0884910	−	0.0336085i
$331$	−245.423			−0.741461			−0.370730	−	0.928741i	$-0.620893\pi$
$331$	−245.423			−0.741461			−0.370730	+	0.928741i	$0.620893\pi$
$332$	−51.2577	−	51.2577i	−0.154391	−	0.154391i
$333$	−18.1362	+	18.1362i	−0.0544631	+	0.0544631i
$334$		−	20.2429i		−	0.0606074i
$335$	290.879	+	130.747i	0.868294	+	0.390289i
$336$	125.035			0.372129
$337$	213.808	+	213.808i	0.634446	+	0.634446i	0.949180	−	0.314734i	$-0.101915\pi$
$337$	213.808	+	213.808i	0.634446	+	0.634446i	−0.314734	+	0.949180i	$0.601915\pi$
$338$	−24.1339	+	24.1339i	−0.0714022	+	0.0714022i
$339$			239.171i			0.705520i
$340$	196.091	−	436.252i	0.576738	−	1.28309i
$341$	121.394			0.355994
$342$	5.86378	+	5.86378i	0.0171455	+	0.0171455i
$343$	255.959	−	255.959i	0.746237	−	0.746237i
$344$			94.0704i			0.273460i
$345$	−50.2270	−	132.247i	−0.145586	−	0.383326i
$346$	65.9092			0.190489
$347$	−160.050	−	160.050i	−0.461239	−	0.461239i	0.437822	−	0.899062i	$-0.355750\pi$
$347$	−160.050	−	160.050i	−0.461239	−	0.461239i	−0.899062	+	0.437822i	$0.855750\pi$
$348$	−167.833	+	167.833i	−0.482279	+	0.482279i
$349$		−	298.009i		−	0.853894i	−0.904277	−	0.426947i	$-0.859589\pi$
$349$		−	298.009i		−	0.853894i	0.904277	−	0.426947i	$-0.140411\pi$
$350$	25.7321	+	28.9898i	0.0735204	+	0.0828280i
$351$	−40.7878			−0.116204
$352$	−118.328	−	118.328i	−0.336159	−	0.336159i
$353$	−22.5199	+	22.5199i	−0.0637957	+	0.0637957i	−0.738285	−	0.674489i	$-0.764364\pi$
$353$	−22.5199	+	22.5199i	−0.0637957	+	0.0637957i	0.674489	+	0.738285i	$0.264364\pi$
$354$			21.9842i			0.0621022i
$355$	317.848	−	120.717i	0.895346	−	0.340049i
$356$	320.424			0.900069
$357$	146.586	+	146.586i	0.410604	+	0.410604i
$358$	−41.2883	+	41.2883i	−0.115330	+	0.115330i
$359$			48.2724i			0.134464i	0.997737	+	0.0672318i	$0.0214167\pi$
$359$			48.2724i			0.134464i	−0.997737	+	0.0672318i	$0.978583\pi$
$360$	34.3485	+	15.4393i	0.0954124	+	0.0428869i
$361$	285.363			0.790480
$362$	−64.3383	−	64.3383i	−0.177730	−	0.177730i
$363$	−9.53801	+	9.53801i	−0.0262755	+	0.0262755i
$364$			149.303i			0.410173i
$365$	−225.505	+	501.691i	−0.617822	+	1.37450i
$366$	−3.25307			−0.00888816
$367$	146.510	+	146.510i	0.399209	+	0.399209i	0.877954	−	0.478745i	$-0.158908\pi$
$367$	146.510	+	146.510i	0.399209	+	0.399209i	−0.478745	+	0.877954i	$0.658908\pi$
$368$	−170.924	+	170.924i	−0.464467	+	0.464467i
$369$		−	2.09082i		−	0.00566617i
$370$	4.82399	+	12.7015i	0.0130378	+	0.0343284i
$371$	−4.80816			−0.0129600
$372$	51.0806	+	51.0806i	0.137313	+	0.137313i
$373$	86.2066	−	86.2066i	0.231117	−	0.231117i	−0.582042	−	0.813159i	$-0.697746\pi$
$373$	86.2066	−	86.2066i	0.231117	−	0.231117i	0.813159	+	0.582042i	$0.197746\pi$
$374$		−	88.4949i		−	0.236617i
$375$	−64.7071	−	206.611i	−0.172552	−	0.550962i
$376$	157.101			0.417822
$377$	−195.081	−	195.081i	−0.517455	−	0.517455i
$378$	−5.69694	+	5.69694i	−0.0150713	+	0.0150713i
$379$		−	210.000i		−	0.554090i	−0.960857	−	0.277045i	$-0.910645\pi$
$379$		−	210.000i		−	0.554090i	0.960857	−	0.277045i	$-0.0893551\pi$
$380$	−158.499	+	60.1975i	−0.417104	+	0.158414i
$381$	−403.237			−1.05837
$382$	10.8082	+	10.8082i	0.0282936	+	0.0282936i
$383$	−10.6311	+	10.6311i	−0.0277575	+	0.0277575i	−0.720849	−	0.693092i	$-0.756248\pi$
$383$	−10.6311	+	10.6311i	−0.0277575	+	0.0277575i	0.693092	+	0.720849i	$0.256248\pi$
$384$		−	132.167i		−	0.344184i
$385$	−252.474	−	113.485i	−0.655778	−	0.294765i
$386$	−114.874			−0.297601
$387$	79.4847	+	79.4847i	0.205387	+	0.205387i
$388$	−95.8990	+	95.8990i	−0.247162	+	0.247162i
$389$		−	535.337i		−	1.37619i	−0.725621	−	0.688094i	$-0.758448\pi$
$389$		−	535.337i		−	1.37619i	0.725621	−	0.688094i	$-0.241552\pi$
$390$	−8.85816	+	19.7071i	−0.0227132	+	0.0505311i
$391$	−400.767			−1.02498
$392$	−44.7401	−	44.7401i	−0.114133	−	0.114133i
$393$	−129.990	+	129.990i	−0.330763	+	0.330763i
$394$		−	43.4643i		−	0.110315i
$395$	43.4847	+	114.495i	0.110088	+	0.289860i
$396$	−132.742			−0.335208
$397$	118.742	+	118.742i	0.299099	+	0.299099i	0.840661	−	0.541562i	$-0.182167\pi$
$397$	118.742	+	118.742i	0.299099	+	0.299099i	−0.541562	+	0.840661i	$0.682167\pi$
$398$	−43.2872	+	43.2872i	−0.108762	+	0.108762i
$399$		−	73.4847i		−	0.184172i
$400$	−276.677	+	245.586i	−0.691691	+	0.613964i
$401$	420.302			1.04813			0.524067	−	0.851677i	$-0.324414\pi$
$401$	420.302			1.04813			0.524067	+	0.851677i	$0.324414\pi$
$402$	24.8286	+	24.8286i	0.0617626	+	0.0617626i
$403$	−59.3735	+	59.3735i	−0.147329	+	0.147329i
$404$			411.814i			1.01934i
$405$	42.0681	−	15.9773i	0.103872	−	0.0394501i
$406$	−54.4949			−0.134224
$407$	−68.6061	−	68.6061i	−0.168565	−	0.168565i
$408$	75.4393	−	75.4393i	0.184900	−	0.184900i
$409$		−	515.110i		−	1.25944i	−0.776823	−	0.629719i	$-0.783170\pi$
$409$		−	515.110i		−	1.25944i	0.776823	−	0.629719i	$-0.216830\pi$
$410$	−1.01021	−	0.454077i	−0.00246391	−	0.00110750i
$411$	408.161			0.993093
$412$	347.974	+	347.974i	0.844597	+	0.844597i
$413$	137.753	−	137.753i	0.333541	−	0.333541i
$414$		−	15.5755i		−	0.0376220i
$415$	−38.1112	+	84.7878i	−0.0918343	+	0.204308i
$416$	115.748			0.278240
$417$	234.136	+	234.136i	0.561478	+	0.561478i
$418$	−22.1816	+	22.1816i	−0.0530661	+	0.0530661i
$419$		−	88.6015i		−	0.211460i	−0.994395	−	0.105730i	$-0.966282\pi$
$419$		−	88.6015i		−	0.211460i	0.994395	−	0.105730i	$-0.0337178\pi$
$420$	−58.4847	−	153.990i	−0.139249	−	0.366642i
$421$	−257.151			−0.610810			−0.305405	−	0.952223i	$-0.598792\pi$
$421$	−257.151			−0.610810			−0.305405	+	0.952223i	$0.598792\pi$
$422$	33.0852	+	33.0852i	0.0784009	+	0.0784009i
$423$	132.742	−	132.742i	0.313812	−	0.313812i
$424$			2.47449i			0.00583605i
$425$	−612.277	−	36.4495i	−1.44065	−	0.0857635i
$426$	37.4347			0.0878749
$427$	20.3837	+	20.3837i	0.0477369	+	0.0477369i
$428$	268.025	−	268.025i	0.626227	−	0.626227i
$429$		−	154.293i		−	0.359657i
$430$	55.6663	−	21.1418i	0.129457	−	0.0491671i
$431$	804.636			1.86690			0.933452	−	0.358702i	$-0.116781\pi$
$431$	804.636			1.86690			0.933452	+	0.358702i	$0.116781\pi$
$432$	−54.3712	−	54.3712i	−0.125859	−	0.125859i
$433$	−344.848	+	344.848i	−0.796416	+	0.796416i	−0.982528	−	0.186113i	$-0.940411\pi$
$433$	−344.848	+	344.848i	−0.796416	+	0.796416i	0.186113	+	0.982528i	$0.440411\pi$
$434$			16.5857i			0.0382159i
$435$	277.621	+	124.788i	0.638209	+	0.286868i
$436$	267.848			0.614330
$437$	100.454	+	100.454i	0.229872	+	0.229872i
$438$	−42.8230	+	42.8230i	−0.0977693	+	0.0977693i
$439$			432.929i			0.986170i	0.869981	+	0.493085i	$0.164131\pi$
$439$			432.929i			0.986170i	−0.869981	+	0.493085i	$0.835869\pi$
$440$	−58.4041	+	129.934i	−0.132737	+	0.295305i
$441$	−75.6061			−0.171442
$442$	43.2827	+	43.2827i	0.0979246	+	0.0979246i
$443$	245.131	−	245.131i	0.553342	−	0.553342i	−0.374062	−	0.927404i	$-0.622035\pi$
$443$	245.131	−	245.131i	0.553342	−	0.553342i	0.927404	+	0.374062i	$0.122035\pi$
$444$		−	57.7367i		−	0.130038i
$445$	−145.893	−	384.136i	−0.327850	−	0.863227i
$446$	75.2577			0.168739
$447$	−103.924	−	103.924i	−0.232492	−	0.232492i
$448$	−188.015	+	188.015i	−0.419676	+	0.419676i
$449$			386.091i			0.859890i	0.902855	+	0.429945i	$0.141467\pi$
$449$			386.091i			0.859890i	−0.902855	+	0.429945i	$0.858533\pi$
$450$	1.41658	−	23.7957i	0.00314796	−	0.0528793i
$451$	7.90918			0.0175370
$452$	−380.702	−	380.702i	−0.842260	−	0.842260i
$453$	−182.449	+	182.449i	−0.402758	+	0.402758i
$454$			113.798i			0.250656i
$455$	178.990	−	67.9796i	0.393384	−	0.149406i
$456$	−37.8184			−0.0829350
$457$	−223.747	−	223.747i	−0.489599	−	0.489599i	0.418580	−	0.908180i	$-0.362528\pi$
$457$	−223.747	−	223.747i	−0.489599	−	0.489599i	−0.908180	+	0.418580i	$0.862528\pi$
$458$	50.3883	−	50.3883i	0.110018	−	0.110018i
$459$		−	127.485i		−	0.277744i
$460$	290.454	+	130.556i	0.631422	+	0.283818i
$461$	−722.620			−1.56751			−0.783753	−	0.621073i	$-0.786697\pi$
$461$	−722.620			−1.56751			−0.783753	+	0.621073i	$0.786697\pi$
$462$	−21.5505	−	21.5505i	−0.0466461	−	0.0466461i
$463$	−129.702	+	129.702i	−0.280133	+	0.280133i	−0.833162	−	0.553029i	$-0.813472\pi$
$463$	−129.702	+	129.702i	−0.280133	+	0.280133i	0.553029	+	0.833162i	$0.313472\pi$
$464$		−	520.095i		−	1.12090i
$465$	37.9796	−	84.4949i	0.0816765	−	0.181709i
$466$	−92.4653			−0.198423
$467$	415.258	+	415.258i	0.889203	+	0.889203i	0.994446	−	0.105244i	$-0.0335623\pi$
$467$	415.258	+	415.258i	0.889203	+	0.889203i	−0.105244	+	0.994446i	$0.533562\pi$
$468$	64.9240	−	64.9240i	0.138726	−	0.138726i
$469$		−	311.151i		−	0.663435i
$470$	−35.3076	−	92.9648i	−0.0751227	−	0.197797i
$471$	−41.2827			−0.0876489
$472$	−70.8934	−	70.8934i	−0.150198	−	0.150198i
$473$	−300.677	+	300.677i	−0.635680	+	0.635680i
$474$			13.4847i			0.0284487i
$475$	144.334	+	162.606i	0.303860	+	0.342329i
$476$	−466.656			−0.980370
$477$	2.09082	+	2.09082i	0.00438326	+	0.00438326i
$478$	77.7163	−	77.7163i	0.162586	−	0.162586i
$479$			304.949i			0.636637i	0.947984	+	0.318318i	$0.103118\pi$
$479$			304.949i			0.636637i	−0.947984	+	0.318318i	$0.896882\pi$
$480$	−119.381	+	45.3406i	−0.248711	+	0.0944595i
$481$	67.1102			0.139522
$482$	22.8286	+	22.8286i	0.0473622	+	0.0473622i
$483$	−97.5959	+	97.5959i	−0.202062	+	0.202062i
$484$		−	30.3643i		−	0.0627361i
$485$	158.631	+	71.3031i	0.327074	+	0.147017i
$486$	4.95459			0.0101946
$487$	−429.318	−	429.318i	−0.881556	−	0.881556i	0.112137	−	0.993693i	$-0.464231\pi$
$487$	−429.318	−	429.318i	−0.881556	−	0.881556i	−0.993693	+	0.112137i	$0.964231\pi$
$488$	10.4903	−	10.4903i	0.0214965	−	0.0214965i
$489$			319.918i			0.654230i
$490$	−16.4199	+	36.5301i	−0.0335100	+	0.0745512i
$491$	−414.318			−0.843825			−0.421912	−	0.906637i	$-0.638641\pi$
$491$	−414.318			−0.843825			−0.421912	+	0.906637i	$0.638641\pi$
$492$	3.32806	+	3.32806i	0.00676435	+	0.00676435i
$493$	609.737	−	609.737i	1.23679	−	1.23679i
$494$		−	21.6980i		−	0.0439230i
$495$	60.4393	+	159.136i	0.122100	+	0.321487i
$496$	−158.293			−0.319139
$497$	−234.565	−	234.565i	−0.471962	−	0.471962i
$498$	−7.23724	+	7.23724i	−0.0145326	+	0.0145326i
$499$			367.585i			0.736643i	0.929699	+	0.368321i	$0.120067\pi$
$499$			367.585i			0.736643i	−0.929699	+	0.368321i	$0.879933\pi$
$500$	431.871	+	225.875i	0.863741	+	0.451750i
$501$	110.313			0.220186
$502$	−74.4485	−	74.4485i	−0.148304	−	0.148304i
$503$	−9.59133	+	9.59133i	−0.0190683	+	0.0190683i	−0.716577	−	0.697508i	$-0.754292\pi$
$503$	−9.59133	+	9.59133i	−0.0190683	+	0.0190683i	0.697508	+	0.716577i	$0.254292\pi$
$504$		−	36.7423i		−	0.0729015i
$505$	493.697	−	187.504i	0.977618	−	0.371295i
$506$	58.9194			0.116441
$507$	−131.518	−	131.518i	−0.259404	−	0.259404i
$508$	641.854	−	641.854i	1.26349	−	1.26349i
$509$			777.489i			1.52748i	0.645522	+	0.763742i	$0.276640\pi$
$509$			777.489i			1.52748i	−0.645522	+	0.763742i	$0.723360\pi$
$510$	−61.5959	−	27.6867i	−0.120776	−	0.0542877i
$511$	536.656			1.05021
$512$	259.376	+	259.376i	0.506593	+	0.506593i
$513$	−31.9546	+	31.9546i	−0.0622897	+	0.0622897i
$514$			14.9398i			0.0290658i
$515$	258.727	−	575.601i	0.502382	−	1.11767i
$516$	−253.040			−0.490387
$517$	502.141	+	502.141i	0.971259	+	0.971259i
$518$	9.37347	−	9.37347i	0.0180955	−	0.0180955i
$519$			359.171i			0.692045i
$520$	−34.9852	−	92.1158i	−0.0672792	−	0.177146i
$521$	321.605			0.617284			0.308642	−	0.951178i	$-0.400125\pi$
$521$	321.605			0.617284			0.308642	+	0.951178i	$0.400125\pi$
$522$	23.6969	+	23.6969i	0.0453964	+	0.0453964i
$523$	−582.454	+	582.454i	−1.11368	+	1.11368i	−0.121030	+	0.992649i	$0.538620\pi$
$523$	−582.454	+	582.454i	−1.11368	+	1.11368i	−0.992649	+	0.121030i	$0.961380\pi$
$524$		−	413.823i		−	0.789738i
$525$	−157.980	+	140.227i	−0.300914	+	0.267099i
$526$	−125.029			−0.237697
$527$	−185.576	−	185.576i	−0.352136	−	0.352136i
$528$	205.677	−	205.677i	0.389539	−	0.389539i
$529$			262.171i			0.495598i
$530$	1.46428	−	0.556128i	0.00276280	−	0.00104930i
$531$	−119.803			−0.225617
$532$	116.969	+	116.969i	0.219867	+	0.219867i
$533$	−3.86836	+	3.86836i	−0.00725772	+	0.00725772i
$534$		−	45.2418i		−	0.0847225i
$535$	−443.353	−	199.283i	−0.828697	−	0.372491i
$536$	−160.132			−0.298753
$537$	−225.000	−	225.000i	−0.418994	−	0.418994i
$538$	109.788	−	109.788i	0.204066	−	0.204066i
$539$		−	286.005i		−	0.530621i
$540$	−41.5301	+	92.3939i	−0.0769076	+	0.171100i
$541$	460.697			0.851566			0.425783	−	0.904825i	$-0.359999\pi$
$541$	460.697			0.851566			0.425783	+	0.904825i	$0.359999\pi$
$542$	29.5709	+	29.5709i	0.0545589	+	0.0545589i
$543$	350.611	−	350.611i	0.645692	−	0.645692i
$544$			361.778i			0.665032i
$545$	−121.955	−	321.106i	−0.223770	−	0.589185i
$546$	21.0806			0.0386092
$547$	−661.778	−	661.778i	−1.20983	−	1.20983i	−0.971081	−	0.238750i	$-0.923262\pi$
$547$	−661.778	−	661.778i	−1.20983	−	1.20983i	−0.238750	−	0.971081i	$-0.576738\pi$
$548$	−649.691	+	649.691i	−1.18557	+	1.18557i
$549$		−	17.7276i		−	0.0322906i
$550$	90.0148	+	5.35867i	0.163663	+	0.00974304i
$551$	−305.666			−0.554748
$552$	50.2270	+	50.2270i	0.0909910	+	0.0909910i
$553$	84.4949	−	84.4949i	0.152794	−	0.152794i
$554$			45.6276i			0.0823602i
$555$	−69.2168	+	26.2883i	−0.124715	+	0.0473663i
$556$	−745.373			−1.34060
$557$	125.909	+	125.909i	0.226049	+	0.226049i	0.811040	−	0.584991i	$-0.198902\pi$
$557$	125.909	+	125.909i	0.226049	+	0.226049i	−0.584991	+	0.811040i	$0.698902\pi$
$558$	7.21225	−	7.21225i	0.0129252	−	0.0129252i
$559$		−	294.120i		−	0.526155i
$560$	329.217	+	147.980i	0.587887	+	0.264249i
$561$	482.252			0.859629
$562$	77.1556	+	77.1556i	0.137288	+	0.137288i
$563$	−200.009	+	200.009i	−0.355256	+	0.355256i	−0.862061	−	0.506805i	$-0.830826\pi$
$563$	−200.009	+	200.009i	−0.355256	+	0.355256i	0.506805	+	0.862061i	$0.330826\pi$
$564$			422.586i			0.749265i
$565$	−283.060	+	629.737i	−0.500992	+	1.11458i
$566$	0.535718			0.000946498
$567$	−31.0454	−	31.0454i	−0.0547538	−	0.0547538i
$568$	−120.717	+	120.717i	−0.212531	+	0.212531i
$569$		−	599.839i		−	1.05420i	−0.849804	−	0.527099i	$-0.823280\pi$
$569$		−	599.839i		−	1.05420i	0.849804	−	0.527099i	$-0.176720\pi$
$570$	8.49948	+	22.3791i	0.0149114	+	0.0392616i
$571$	−247.970			−0.434274			−0.217137	−	0.976141i	$-0.569672\pi$
$571$	−247.970			−0.434274			−0.217137	+	0.976141i	$0.569672\pi$
$572$	245.596	+	245.596i	0.429363	+	0.429363i
$573$	−58.8990	+	58.8990i	−0.102791	+	0.102791i
$574$			1.08061i			0.00188260i
$575$	24.2679	−	407.650i	0.0422050	−	0.708957i
$576$	163.515			0.283881
$577$	−292.121	−	292.121i	−0.506276	−	0.506276i	0.407105	−	0.913381i	$-0.366538\pi$
$577$	−292.121	−	292.121i	−0.506276	−	0.506276i	−0.913381	+	0.407105i	$0.866538\pi$
$578$	−70.3314	+	70.3314i	−0.121681	+	0.121681i
$579$		−	626.005i		−	1.08118i
$580$	−640.535	+	243.272i	−1.10437	+	0.419435i
$581$	90.6969			0.156105
$582$	13.5403	+	13.5403i	0.0232651	+	0.0232651i
$583$	−7.90918	+	7.90918i	−0.0135664	+	0.0135664i
$584$		−	276.186i		−	0.472922i
$585$	−107.394	−	48.2724i	−0.183579	−	0.0825170i
$586$	43.4051			0.0740702
$587$	611.217	+	611.217i	1.04126	+	1.04126i	0.999112	+	0.0421437i	$0.0134187\pi$
$587$	611.217	+	611.217i	1.04126	+	1.04126i	0.0421437	+	0.999112i	$0.486581\pi$
$588$	120.346	−	120.346i	0.204670	−	0.204670i
$589$			93.0306i			0.157947i
$590$	−26.0183	+	57.8842i	−0.0440989	+	0.0981088i
$591$	236.858			0.400775
$592$	89.4597	+	89.4597i	0.151114	+	0.151114i
$593$	524.742	−	524.742i	0.884894	−	0.884894i	−0.109133	−	0.994027i	$-0.534807\pi$
$593$	524.742	−	524.742i	0.884894	−	0.884894i	0.994027	+	0.109133i	$0.0348074\pi$
$594$			18.7423i			0.0315528i
$595$	212.474	+	559.444i	0.357100	+	0.940242i
$596$	330.842			0.555105
$597$	−235.893	−	235.893i	−0.395131	−	0.395131i
$598$	−28.8173	+	28.8173i	−0.0481895	+	0.0481895i
$599$		−	368.858i		−	0.615790i	−0.951420	−	0.307895i	$-0.900375\pi$
$599$		−	368.858i		−	0.615790i	0.951420	−	0.307895i	$-0.0996245\pi$
$600$	72.1668	+	81.3031i	0.120278	+	0.135505i
$601$	932.484			1.55155			0.775777	−	0.631007i	$-0.217358\pi$
$601$	932.484			1.55155			0.775777	+	0.631007i	$0.217358\pi$
$602$	−41.0806	−	41.0806i	−0.0682402	−	0.0682402i
$603$	−135.303	+	135.303i	−0.224383	+	0.224383i
$604$		−	580.829i		−	0.961637i
$605$	−36.4018	+	13.8252i	−0.0601682	+	0.0228517i
$606$	58.1454			0.0959495
$607$	513.611	+	513.611i	0.846146	+	0.846146i	0.989650	−	0.143504i	$-0.0458369\pi$
$607$	513.611	+	513.611i	0.846146	+	0.846146i	−0.143504	+	0.989650i	$0.545837\pi$
$608$	90.6811	−	90.6811i	0.149147	−	0.149147i
$609$		−	296.969i		−	0.487634i
$610$	−8.56530	−	3.85002i	−0.0140415	−	0.00631150i
$611$	−491.192			−0.803915
$612$	202.924	+	202.924i	0.331575	+	0.331575i
$613$	−615.287	+	615.287i	−1.00373	+	1.00373i	−0.00373821	+	0.999993i	$0.501190\pi$
$613$	−615.287	+	615.287i	−1.00373	+	1.00373i	−0.999993	+	0.00373821i	$0.998810\pi$
$614$		−	56.1725i		−	0.0914861i
$615$	2.47449	−	5.50510i	0.00402356	−	0.00895139i
$616$	138.990			0.225633
$617$	546.752	+	546.752i	0.886145	+	0.886145i	0.994150	−	0.108005i	$-0.0344463\pi$
$617$	546.752	+	546.752i	0.886145	+	0.886145i	−0.108005	+	0.994150i	$0.534446\pi$
$618$	49.1316	−	49.1316i	0.0795010	−	0.0795010i
$619$			152.869i			0.246962i	0.992347	+	0.123481i	$0.0394058\pi$
$619$			152.869i			0.246962i	−0.992347	+	0.123481i	$0.960594\pi$
$620$	74.0408	+	194.949i	0.119421	+	0.314434i
$621$	84.8786			0.136680
$622$	−131.768	−	131.768i	−0.211846	−	0.211846i
$623$	−283.485	+	283.485i	−0.455032	+	0.455032i
$624$			201.192i			0.322423i
$625$	74.1510	−	620.586i	0.118642	−	0.992937i
$626$	−46.0158			−0.0735077
$627$	−120.879	−	120.879i	−0.192789	−	0.192789i
$628$	65.7117	−	65.7117i	0.104637	−	0.104637i
$629$			209.757i			0.333477i
$630$	−21.7423	+	8.25765i	−0.0345117	+	0.0131074i
$631$	−41.4847			−0.0657444			−0.0328722	−	0.999460i	$-0.510465\pi$
$631$	−41.4847			−0.0657444			−0.0328722	+	0.999460i	$0.510465\pi$
$632$	−43.4847	−	43.4847i	−0.0688049	−	0.0688049i
$633$	−180.297	+	180.297i	−0.284830	+	0.284830i
$634$		−	48.8969i		−	0.0771245i
$635$	−1061.72	−	477.233i	−1.67200	−	0.751547i
$636$	−6.65612			−0.0104656
$637$	139.884	+	139.884i	0.219598	+	0.219598i
$638$	−89.6413	+	89.6413i	−0.140504	+	0.140504i
$639$			204.000i			0.319249i
$640$	156.420	−	347.994i	0.244406	−	0.543741i
$641$	47.2122			0.0736541			0.0368270	−	0.999322i	$-0.488275\pi$
$641$	47.2122			0.0736541			0.0368270	+	0.999322i	$0.488275\pi$
$642$	−37.8434	−	37.8434i	−0.0589461	−	0.0589461i
$643$	460.372	−	460.372i	0.715976	−	0.715976i	−0.251803	−	0.967779i	$-0.581023\pi$
$643$	460.372	−	460.372i	0.715976	−	0.715976i	0.967779	+	0.251803i	$0.0810234\pi$
$644$		−	310.697i		−	0.482449i
$645$	115.212	+	303.353i	0.178624	+	0.470315i
$646$	67.8184			0.104982
$647$	−281.287	−	281.287i	−0.434756	−	0.434756i	0.455487	−	0.890243i	$-0.349465\pi$
$647$	−281.287	−	281.287i	−0.434756	−	0.434756i	−0.890243	+	0.455487i	$0.849465\pi$
$648$	−15.9773	+	15.9773i	−0.0246563	+	0.0246563i
$649$		−	453.192i		−	0.698293i
$650$	−46.6469	+	41.4051i	−0.0717645	+	0.0637002i
$651$	−90.3837			−0.138838
$652$	−509.231	−	509.231i	−0.781029	−	0.781029i
$653$	89.8230	−	89.8230i	0.137554	−	0.137554i	−0.634977	−	0.772531i	$-0.718990\pi$
$653$	89.8230	−	89.8230i	0.137554	−	0.137554i	0.772531	+	0.634977i	$0.218990\pi$
$654$		−	37.8184i		−	0.0578263i
$655$	−496.106	+	188.419i	−0.757413	+	0.287662i
$656$	−10.3133			−0.0157214
$657$	−233.363	−	233.363i	−0.355195	−	0.355195i
$658$	−68.6061	+	68.6061i	−0.104265	+	0.104265i
$659$			1081.24i			1.64072i	0.571844	+	0.820362i	$0.306228\pi$
$659$			1081.24i			1.64072i	−0.571844	+	0.820362i	$0.693772\pi$
$660$	−349.510	−	157.101i	−0.529560	−	0.238032i
$661$	−632.393			−0.956721			−0.478361	−	0.878163i	$-0.658769\pi$
$661$	−632.393			−0.956721			−0.478361	+	0.878163i	$0.658769\pi$
$662$	−55.1577	−	55.1577i	−0.0833197	−	0.0833197i
$663$	−235.868	+	235.868i	−0.355759	+	0.355759i
$664$		−	46.6765i		−	0.0702960i
$665$	86.9694	−	193.485i	0.130781	−	0.290954i
$666$	−8.15205			−0.0122403
$667$	405.959	+	405.959i	0.608634	+	0.608634i
$668$	−175.591	+	175.591i	−0.262861	+	0.262861i
$669$			410.116i			0.613028i
$670$	35.9888	+	94.7582i	0.0537146	+	0.141430i
$671$	67.0602			0.0999407
$672$	88.1010	+	88.1010i	0.131103	+	0.131103i
$673$	233.293	−	233.293i	0.346646	−	0.346646i	−0.512213	−	0.858859i	$-0.671174\pi$
$673$	233.293	−	233.293i	0.346646	−	0.346646i	0.858859	+	0.512213i	$0.171174\pi$
$674$			96.1046i			0.142588i
$675$	129.674	+	7.71964i	0.192110	+	0.0114365i
$676$	418.687			0.619359
$677$	−48.3883	−	48.3883i	−0.0714745	−	0.0714745i	0.670466	−	0.741940i	$-0.266094\pi$
$677$	−48.3883	−	48.3883i	−0.0714745	−	0.0714745i	−0.741940	+	0.670466i	$0.766094\pi$
$678$	−53.7526	+	53.7526i	−0.0792810	+	0.0792810i
$679$		−	169.687i		−	0.249907i
$680$	287.914	−	109.348i	0.423403	−	0.160807i
$681$	−620.141			−0.910633
$682$	27.2827	+	27.2827i	0.0400039	+	0.0400039i
$683$	213.410	−	213.410i	0.312459	−	0.312459i	−0.533402	−	0.845862i	$-0.679087\pi$
$683$	213.410	−	213.410i	0.312459	−	0.312459i	0.845862	+	0.533402i	$0.179087\pi$
$684$		−	101.728i		−	0.148724i
$685$	1074.69	+	483.060i	1.56888	+	0.705197i
$686$	115.051			0.167713
$687$	274.590	+	274.590i	0.399695	+	0.399695i
$688$	392.070	−	392.070i	0.569870	−	0.569870i
$689$		−	7.73673i		−	0.0112289i
$690$	18.4337	−	41.0102i	0.0267155	−	0.0594351i
$691$	151.121			0.218700			0.109350	−	0.994003i	$-0.465123\pi$
$691$	151.121			0.218700			0.109350	+	0.994003i	$0.465123\pi$
$692$	−571.712	−	571.712i	−0.826173	−	0.826173i
$693$	117.439	−	117.439i	0.169465	−	0.169465i
$694$		−	71.9408i		−	0.103661i
$695$	339.378	+	893.580i	0.488314	+	1.28573i
$696$	−152.833			−0.219588
$697$	−12.0908	−	12.0908i	−0.0173469	−	0.0173469i
$698$	66.9760	−	66.9760i	0.0959542	−	0.0959542i
$699$		−	503.889i		−	0.720871i
$700$	28.2577	−	474.671i	0.0403681	−	0.678101i
$701$	−745.680			−1.06374			−0.531869	−	0.846827i	$-0.678510\pi$
$701$	−745.680			−1.06374			−0.531869	+	0.846827i	$0.678510\pi$
$702$	−9.16684	−	9.16684i	−0.0130582	−	0.0130582i
$703$	52.5765	−	52.5765i	0.0747888	−	0.0747888i
$704$			618.549i			0.878621i
$705$	506.611	−	192.409i	0.718597	−	0.272920i
$706$	−10.1225			−0.0143378
$707$	−364.338	−	364.338i	−0.515330	−	0.515330i
$708$	190.696	−	190.696i	0.269345	−	0.269345i
$709$			719.049i			1.01417i	0.861895	+	0.507087i	$0.169278\pi$
$709$			719.049i			1.01417i	−0.861895	+	0.507087i	$0.830722\pi$
$710$	98.5653	+	44.3041i	0.138824	+	0.0624001i
$711$	−73.4847			−0.103354
$712$	145.893	+	145.893i	0.204906	+	0.204906i
$713$	123.555	−	123.555i	0.173289	−	0.173289i
$714$			65.8888i			0.0922812i
$715$	182.606	−	406.252i	0.255393	−	0.568185i
$716$	716.288			1.00040
$717$	423.514	+	423.514i	0.590675	+	0.590675i
$718$	−10.8490	+	10.8490i	−0.0151100	+	0.0151100i
$719$		−	605.271i		−	0.841824i	−0.907101	−	0.420912i	$-0.861710\pi$
$719$		−	605.271i		−	0.841824i	0.907101	−	0.420912i	$-0.138290\pi$
$720$	−78.8105	−	207.507i	−0.109459	−	0.288205i
$721$	−615.716			−0.853975
$722$	64.1339	+	64.1339i	0.0888282	+	0.0888282i
$723$	−124.404	+	124.404i	−0.172067	+	0.172067i
$724$			1116.17i			1.54167i
$725$	583.287	+	657.131i	0.804534	+	0.906387i
$726$	−4.28724			−0.00590529
$727$	−246.126	−	246.126i	−0.338550	−	0.338550i	0.517271	−	0.855821i	$-0.326948\pi$
$727$	−246.126	−	246.126i	−0.338550	−	0.338550i	−0.855821	+	0.517271i	$0.826948\pi$
$728$	−67.9796	+	67.9796i	−0.0933786	+	0.0933786i
$729$			27.0000i			0.0370370i
$730$	−163.434	+	62.0714i	−0.223882	+	0.0850294i
$731$	919.292			1.25758
$732$	28.2179	+	28.2179i	0.0385490	+	0.0385490i
$733$	−270.763	+	270.763i	−0.369390	+	0.369390i	−0.867255	−	0.497865i	$-0.834118\pi$
$733$	−270.763	+	270.763i	−0.369390	+	0.369390i	0.497865	+	0.867255i	$0.334118\pi$
$734$			65.8546i			0.0897202i
$735$	−199.070	−	89.4801i	−0.270844	−	0.121742i
$736$	−240.869			−0.327268
$737$	−511.828	−	511.828i	−0.694474	−	0.694474i
$738$	0.469900	−	0.469900i	0.000636721	−	0.000636721i
$739$		−	515.666i		−	0.697789i	−0.937162	−	0.348895i	$-0.886557\pi$
$739$		−	515.666i		−	0.697789i	0.937162	−	0.348895i	$-0.113443\pi$
$740$	68.3316	−	152.020i	0.0923400	−	0.205433i
$741$	118.243			0.159572
$742$	−1.08061	−	1.08061i	−0.00145635	−	0.00145635i
$743$	420.702	−	420.702i	0.566220	−	0.566220i	−0.364847	−	0.931067i	$-0.618879\pi$
$743$	420.702	−	420.702i	0.566220	−	0.566220i	0.931067	+	0.364847i	$0.118879\pi$
$744$			46.5153i			0.0625206i
$745$	−150.637	−	396.626i	−0.202197	−	0.532383i
$746$	38.7490			0.0519424
$747$	−39.4393	−	39.4393i	−0.0527969	−	0.0527969i
$748$	−767.626	+	767.626i	−1.02624	+	1.02624i
$749$			474.252i			0.633180i
$750$	31.8921	−	60.9773i	0.0425228	−	0.0813031i
$751$	−859.787			−1.14486			−0.572428	−	0.819955i	$-0.693998\pi$
$751$	−859.787			−1.14486			−0.572428	+	0.819955i	$0.693998\pi$
$752$	−654.772	−	654.772i	−0.870707	−	0.870707i
$753$	405.706	−	405.706i	0.538786	−	0.538786i
$754$		−	87.6867i		−	0.116295i
$755$	−696.318	+	264.459i	−0.922275	+	0.350276i
$756$	98.8332			0.130732
$757$	−956.075	−	956.075i	−1.26298	−	1.26298i	−0.949642	−	0.313337i	$-0.898553\pi$
$757$	−956.075	−	956.075i	−1.26298	−	1.26298i	−0.313337	−	0.949642i	$-0.601447\pi$
$758$	47.1964	−	47.1964i	0.0622644	−	0.0622644i
$759$			321.081i			0.423031i
$760$	−99.5755	−	44.7582i	−0.131020	−	0.0588923i
$761$	−322.758			−0.424124			−0.212062	−	0.977256i	$-0.568018\pi$
$761$	−322.758			−0.424124			−0.212062	+	0.977256i	$0.568018\pi$
$762$	−90.6255	−	90.6255i	−0.118931	−	0.118931i
$763$	−236.969	+	236.969i	−0.310576	+	0.310576i
$764$		−	187.505i		−	0.245426i
$765$	150.879	−	335.666i	0.197227	−	0.438780i
$766$	−4.77858			−0.00623835
$767$	221.655	+	221.655i	0.288990	+	0.288990i
$768$	−237.316	+	237.316i	−0.309005	+	0.309005i
$769$			692.402i			0.900393i	0.892930	+	0.450196i	$0.148646\pi$
$769$			692.402i			0.900393i	−0.892930	+	0.450196i	$0.851354\pi$
$770$	−31.2372	−	82.2474i	−0.0405678	−	0.106815i
$771$	−81.4143			−0.105596
$772$	996.444	+	996.444i	1.29073	+	1.29073i
$773$	375.226	−	375.226i	0.485415	−	0.485415i	−0.421441	−	0.906856i	$-0.638475\pi$
$773$	375.226	−	375.226i	0.485415	−	0.485415i	0.906856	+	0.421441i	$0.138475\pi$
$774$			35.7276i			0.0461596i
$775$	200.000	−	177.526i	0.258065	−	0.229065i
$776$	−87.3281			−0.112536
$777$	51.0806	+	51.0806i	0.0657408	+	0.0657408i
$778$	120.314	−	120.314i	0.154646	−	0.154646i
$779$			6.06123i			0.00778078i
$780$	247.782	−	94.1066i	0.317669	−	0.120650i
$781$	−771.696			−0.988087
$782$	−90.0704	−	90.0704i	−0.115180	−	0.115180i
$783$	−129.136	+	129.136i	−0.164925	+	0.164925i
$784$			372.939i			0.475687i
$785$	−108.697	−	48.8582i	−0.138467	−	0.0622397i
$786$	−58.4291			−0.0743373
$787$	910.990	+	910.990i	1.15755	+	1.15755i	0.985001	+	0.172546i	$0.0551993\pi$
$787$	910.990	+	910.990i	1.15755	+	1.15755i	0.172546	+	0.985001i	$0.444801\pi$
$788$	−377.019	+	377.019i	−0.478451	+	0.478451i
$789$		−	681.342i		−	0.863551i
$790$	−15.9592	+	35.5051i	−0.0202015	+	0.0449432i
$791$	673.626			0.851613
$792$	−60.4393	−	60.4393i	−0.0763122	−	0.0763122i
$793$	−32.7990	+	32.7990i	−0.0413606	+	0.0413606i
$794$			53.3735i			0.0672210i
$795$	3.03062	+	7.97959i	0.00381209	+	0.0100372i
$796$	750.967			0.943426
$797$	−7.21683	−	7.21683i	−0.00905500	−	0.00905500i	0.702565	−	0.711620i	$-0.252038\pi$
$797$	−7.21683	−	7.21683i	−0.00905500	−	0.00905500i	−0.711620	+	0.702565i	$0.752038\pi$
$798$	16.5153	−	16.5153i	0.0206959	−	0.0206959i
$799$		−	1535.25i		−	1.92147i
$800$	−367.991	−	21.9069i	−0.459989	−	0.0273836i
$801$	246.545			0.307796
$802$	94.4607	+	94.4607i	0.117781	+	0.117781i
$803$	882.772	−	882.772i	1.09934	−	1.09934i
$804$		−	430.738i		−	0.535743i
$805$	−372.474	+	141.464i	−0.462701	+	0.175732i
$806$	−26.6878			−0.0331114
$807$	598.287	+	598.287i	0.741372	+	0.741372i
$808$	−187.504	+	187.504i	−0.232059	+	0.232059i
$809$		−	150.000i		−	0.185414i	−0.995693	−	0.0927070i	$-0.970448\pi$
$809$		−	150.000i		−	0.185414i	0.995693	−	0.0927070i	$-0.0295520\pi$
$810$	13.0454	+	5.86378i	0.0161054	+	0.00723923i
$811$	1336.85			1.64839			0.824197	−	0.566304i	$-0.191627\pi$
$811$	1336.85			1.64839			0.824197	+	0.566304i	$0.191627\pi$
$812$	472.702	+	472.702i	0.582145	+	0.582145i
$813$	−161.146	+	161.146i	−0.198212	+	0.198212i
$814$		−	30.8377i		−	0.0378842i
$815$	−378.624	+	842.343i	−0.464570	+	1.03355i
$816$	−628.838			−0.770634
$817$	−230.424	−	230.424i	−0.282037	−	0.282037i
$818$	115.768	−	115.768i	0.141526	−	0.141526i
$819$			114.879i			0.140267i
$820$	4.82399	+	12.7015i	0.00588291	+	0.0154897i
$821$	−33.8934			−0.0412830			−0.0206415	−	0.999787i	$-0.506571\pi$
$821$	−33.8934			−0.0412830			−0.0206415	+	0.999787i	$0.506571\pi$
$822$	91.7321	+	91.7321i	0.111596	+	0.111596i
$823$	481.631	−	481.631i	0.585214	−	0.585214i	−0.351117	−	0.936331i	$-0.614198\pi$
$823$	481.631	−	481.631i	0.585214	−	0.585214i	0.936331	+	0.351117i	$0.114198\pi$
$824$			316.874i			0.384556i
$825$	−29.2020	+	490.535i	−0.0353964	+	0.594587i
$826$	61.9184			0.0749617
$827$	350.756	+	350.756i	0.424131	+	0.424131i	0.886623	−	0.462492i	$-0.153045\pi$
$827$	350.756	+	350.756i	0.424131	+	0.424131i	−0.462492	+	0.886623i	$0.653045\pi$
$828$	−135.106	+	135.106i	−0.163171	+	0.163171i
$829$		−	697.423i		−	0.841283i	−0.907227	−	0.420641i	$-0.861805\pi$
$829$		−	697.423i		−	0.841283i	0.907227	−	0.420641i	$-0.138195\pi$
$830$	−27.6209	+	10.4903i	−0.0332782	+	0.0126389i
$831$	−248.647			−0.299214
$832$	−302.531	−	302.531i	−0.363619	−	0.363619i
$833$	−437.217	+	437.217i	−0.524870	+	0.524870i
$834$			105.242i			0.126189i
$835$	290.454	+	130.556i	0.347849	+	0.156355i
$836$	384.817			0.460308
$837$	39.3031	+	39.3031i	0.0469571	+	0.0469571i
$838$	19.9127	−	19.9127i	0.0237622	−	0.0237622i
$839$			72.3724i			0.0862604i	0.999069	+	0.0431302i	$0.0137330\pi$
$839$			72.3724i			0.0862604i	−0.999069	+	0.0431302i	$0.986267\pi$
$840$	43.4847	−	96.7423i	0.0517675	−	0.115169i
$841$	−394.271			−0.468813
$842$	−57.7934	−	57.7934i	−0.0686382	−	0.0686382i
$843$	−420.459	+	420.459i	−0.498765	+	0.498765i
$844$		−	573.978i		−	0.680068i
$845$	−190.633	−	501.936i	−0.225602	−	0.594008i
$846$	59.6663			0.0705276
$847$	26.8638	+	26.8638i	0.0317164	+	0.0317164i
$848$	10.3133	−	10.3133i	0.0121619	−	0.0121619i
$849$			2.91939i			0.00343862i
$850$	−129.414	−	145.798i	−0.152252	−	0.171527i
$851$	−139.655			−0.164107
$852$	−324.717	−	324.717i	−0.381124	−	0.381124i
$853$	−74.5699	+	74.5699i	−0.0874207	+	0.0874207i	−0.749465	−	0.662044i	$-0.769689\pi$
$853$	−74.5699	+	74.5699i	−0.0874207	+	0.0874207i	0.662044	+	0.749465i	$0.269689\pi$
$854$			9.16225i			0.0107286i
$855$	−121.955	+	46.3179i	−0.142637	+	0.0541729i
$856$	244.070			0.285129
$857$	−293.176	−	293.176i	−0.342096	−	0.342096i	0.515059	−	0.857155i	$-0.327770\pi$
$857$	−293.176	−	293.176i	−0.342096	−	0.342096i	−0.857155	+	0.515059i	$0.827770\pi$
$858$	34.6765	−	34.6765i	0.0404155	−	0.0404155i
$859$		−	786.867i		−	0.916027i	−0.888945	−	0.458014i	$-0.848561\pi$
$859$		−	786.867i		−	0.916027i	0.888945	−	0.458014i	$-0.151439\pi$
$860$	−666.252	−	299.473i	−0.774712	−	0.348225i
$861$	−5.88877			−0.00683946
$862$	180.838	+	180.838i	0.209789	+	0.209789i
$863$	−1072.68	+	1072.68i	−1.24297	+	1.24297i	−0.284204	+	0.958764i	$0.591729\pi$
$863$	−1072.68	+	1072.68i	−1.24297	+	1.24297i	−0.958764	+	0.284204i	$0.908271\pi$
$864$		−	76.6209i		−	0.0886816i
$865$	−425.081	+	945.696i	−0.491423	+	1.09329i
$866$	−155.006			−0.178990
$867$	−383.270	−	383.270i	−0.442065	−	0.442065i
$868$	143.868	−	143.868i	0.165747	−	0.165747i
$869$		−	277.980i		−	0.319884i
$870$	34.3485	+	90.4393i	0.0394810	+	0.103953i
$871$	500.667			0.574819
$872$	121.955	+	121.955i	0.139856	+	0.139856i
$873$	−73.7878	+	73.7878i	−0.0845221	+	0.0845221i
$874$			45.1531i			0.0516626i
$875$	−581.918	+	182.247i	−0.665050	+	0.208283i
$876$	742.913			0.848074
$877$	239.460	+	239.460i	0.273044	+	0.273044i	0.830324	−	0.557280i	$-0.188155\pi$
$877$	239.460	+	239.460i	0.273044	+	0.273044i	−0.557280	+	0.830324i	$0.688155\pi$
$878$	−97.2985	+	97.2985i	−0.110818	+	0.110818i
$879$			236.536i			0.269096i
$880$	784.964	−	298.126i	0.892004	−	0.338780i
$881$	62.8490			0.0713382			0.0356691	−	0.999364i	$-0.488644\pi$
$881$	62.8490			0.0713382			0.0356691	+	0.999364i	$0.488644\pi$
$882$	−16.9921	−	16.9921i	−0.0192654	−	0.0192654i
$883$	−158.061	+	158.061i	−0.179005	+	0.179005i	−0.790922	−	0.611917i	$-0.790399\pi$
$883$	−158.061	+	158.061i	−0.179005	+	0.179005i	0.611917	+	0.790922i	$0.290399\pi$
$884$		−	750.888i		−	0.849421i
$885$	−315.439	−	141.787i	−0.356429	−	0.160211i
$886$	110.184			0.124361
$887$	30.2066	+	30.2066i	0.0340548	+	0.0340548i	0.723929	−	0.689874i	$-0.242334\pi$
$887$	30.2066	+	30.2066i	0.0340548	+	0.0340548i	−0.689874	+	0.723929i	$0.742334\pi$
$888$	26.2883	−	26.2883i	0.0296039	−	0.0296039i
$889$			1135.72i			1.27752i
$890$	53.5439	−	119.121i	0.0601616	−	0.133844i
$891$	−102.136			−0.114631
$892$	−652.803	−	652.803i	−0.731841	−	0.731841i
$893$	−384.817	+	384.817i	−0.430926	+	0.430926i
$894$		−	46.7128i		−	0.0522514i
$895$	−326.135	−	858.712i	−0.364397	−	0.959454i
$896$	−372.247			−0.415455
$897$	−157.040	−	157.040i	−0.175072	−	0.175072i
$898$	−86.7719	+	86.7719i	−0.0966280	+	0.0966280i
$899$			375.959i			0.418197i
$900$	−218.697	+	194.121i	−0.242997	+	0.215690i
$901$	24.1816			0.0268387
$902$	1.77755	+	1.77755i	0.00197067	+	0.00197067i
$903$	223.868	−	223.868i	0.247916	−	0.247916i
$904$		−	346.677i		−	0.383492i
$905$	1338.10	−	508.207i	1.47857	−	0.561554i
$906$	−82.0092			−0.0905179
$907$	571.342	+	571.342i	0.629925	+	0.629925i	0.948049	−	0.318124i	$-0.103053\pi$
$907$	571.342	+	571.342i	0.629925	+	0.629925i	−0.318124	+	0.948049i	$0.603053\pi$
$908$	987.110	−	987.110i	1.08713	−	1.08713i
$909$			316.863i			0.348584i
$910$	55.5051	+	24.9490i	0.0609946	+	0.0274165i
$911$	173.362			0.190299			0.0951494	−	0.995463i	$-0.469667\pi$
$911$	173.362			0.190299			0.0951494	+	0.995463i	$0.469667\pi$
$912$	157.621	+	157.621i	0.172830	+	0.172830i
$913$	149.192	−	149.192i	0.163408	−	0.163408i
$914$		−	100.572i		−	0.110035i
$915$	20.9806	−	46.6765i	0.0229296	−	0.0510126i
$916$	−874.159			−0.954322
$917$	366.116	+	366.116i	0.399254	+	0.399254i
$918$	28.6515	−	28.6515i	0.0312108	−	0.0312108i
$919$			1147.42i			1.24856i	0.781202	+	0.624278i	$0.214607\pi$
$919$			1147.42i			1.24856i	−0.781202	+	0.624278i	$0.785393\pi$
$920$	72.8036	+	191.691i	0.0791343	+	0.208360i
$921$	306.111			0.332368
$922$	−162.405	−	162.405i	−0.176144	−	0.176144i
$923$	377.435	−	377.435i	0.408922	−	0.408922i
$924$			373.868i			0.404619i
$925$	−213.360	−	12.7015i	−0.230659	−	0.0137314i
$926$	−58.2995			−0.0629584
$927$	267.742	+	267.742i	0.288827	+	0.288827i
$928$	366.464	−	366.464i	0.394897	−	0.394897i
$929$		−	220.293i		−	0.237129i	−0.992946	−	0.118565i	$-0.962171\pi$
$929$		−	220.293i		−	0.237129i	0.992946	−	0.118565i	$-0.0378292\pi$
$930$	27.5255	−	10.4541i	0.0295973	−	0.0112409i
$931$	219.181			0.235425
$932$	802.066	+	802.066i	0.860586	+	0.860586i
$933$	718.070	−	718.070i	0.769636	−	0.769636i
$934$			186.654i			0.199844i
$935$	1269.77	+	570.747i	1.35804	+	0.610425i
$936$	59.1214			0.0631639
$937$	−396.090	−	396.090i	−0.422721	−	0.422721i	0.463418	−	0.886140i	$-0.346623\pi$
$937$	−396.090	−	396.090i	−0.422721	−	0.422721i	−0.886140	+	0.463418i	$0.846623\pi$
$938$	69.9296	−	69.9296i	0.0745518	−	0.0745518i
$939$		−	250.763i		−	0.267053i
$940$	−500.132	+	1112.67i	−0.532055	+	1.18369i
$941$	185.771			0.197419			0.0987093	−	0.995116i	$-0.468529\pi$
$941$	185.771			0.197419			0.0987093	+	0.995116i	$0.468529\pi$
$942$	−9.27806	−	9.27806i	−0.00984932	−	0.00984932i
$943$	8.04999	−	8.04999i	0.00853658	−	0.00853658i
$944$			590.944i			0.626000i
$945$	−45.0000	−	118.485i	−0.0476190	−	0.125381i
$946$	−135.151			−0.142866
$947$	−845.190	−	845.190i	−0.892492	−	0.892492i	0.102265	−	0.994757i	$-0.467391\pi$
$947$	−845.190	−	845.190i	−0.892492	−	0.892492i	−0.994757	+	0.102265i	$0.967391\pi$
$948$	116.969	−	116.969i	0.123385	−	0.123385i
$949$			863.523i			0.909930i
$950$	−4.10664	+	68.9831i	−0.00432278	+	0.0726138i
$951$	266.463			0.280193
$952$	−212.474	−	212.474i	−0.223187	−	0.223187i
$953$	−630.499	+	630.499i	−0.661594	+	0.661594i	−0.955756	−	0.294161i	$-0.904960\pi$
$953$	−630.499	+	630.499i	−0.661594	+	0.661594i	0.294161	+	0.955756i	$0.404960\pi$
$954$			0.939800i			0.000985115i
$955$	−224.788	+	85.3735i	−0.235380	+	0.0893963i
$956$	−1348.26			−1.41031
$957$	−488.499	−	488.499i	−0.510449	−	0.510449i
$958$	−68.5357	+	68.5357i	−0.0715404	+	0.0715404i
$959$		−	1149.58i		−	1.19873i
$960$	430.535	+	193.521i	0.448474	+	0.201584i
$961$	−846.576			−0.880932
$962$	15.0827	+	15.0827i	0.0156785	+	0.0156785i
$963$	206.227	−	206.227i	0.214151	−	0.214151i
$964$		−	396.041i		−	0.410831i
$965$	740.879	−	1648.27i	0.767750	−	1.70805i
$966$	−43.8684			−0.0454124
$967$	−381.690	−	381.690i	−0.394716	−	0.394716i	0.481649	−	0.876364i	$-0.340038\pi$
$967$	−381.690	−	381.690i	−0.394716	−	0.394716i	−0.876364	+	0.481649i	$0.840038\pi$
$968$	13.8252	−	13.8252i	0.0142823	−	0.0142823i
$969$			369.576i			0.381399i
$970$	19.6265	+	51.6765i	0.0202335	+	0.0532748i
$971$	−1000.44			−1.03032			−0.515159	−	0.857095i	$-0.672267\pi$
$971$	−1000.44			−1.03032			−0.515159	+	0.857095i	$0.672267\pi$
$972$	−42.9773	−	42.9773i	−0.0442153	−	0.0442153i
$973$	659.444	−	659.444i	0.677743	−	0.677743i
$974$		−	192.974i		−	0.198125i
$975$	−225.637	−	254.202i	−0.231422	−	0.260720i
$976$	−87.4439			−0.0895941
$977$	593.662	+	593.662i	0.607637	+	0.607637i	0.942328	−	0.334691i	$-0.108632\pi$
$977$	593.662	+	593.662i	0.607637	+	0.607637i	−0.334691	+	0.942328i	$0.608632\pi$
$978$	−71.9000	+	71.9000i	−0.0735174	+	0.0735174i
$979$			932.636i			0.952641i
$980$	459.301	−	174.441i	0.468674	−	0.178001i
$981$	206.091			0.210082
$982$	−93.1158	−	93.1158i	−0.0948226	−	0.0948226i
$983$	−1217.34	+	1217.34i	−1.23839	+	1.23839i	−0.277731	+	0.960659i	$0.589582\pi$
$983$	−1217.34	+	1217.34i	−1.23839	+	1.23839i	−0.960659	+	0.277731i	$0.910418\pi$
$984$			3.03062i			0.00307989i
$985$	623.646	+	280.322i	0.633143	+	0.284591i
$986$	274.070			0.277962
$987$	−373.868	−	373.868i	−0.378793	−	0.378793i
$988$	−188.213	+	188.213i	−0.190499	+	0.190499i
$989$			612.059i			0.618867i
$990$	−22.1816	+	49.3485i	−0.0224057	+	0.0498469i
$991$	−544.061			−0.549002			−0.274501	−	0.961587i	$-0.588513\pi$
$991$	−544.061			−0.549002			−0.274501	+	0.961587i	$0.588513\pi$
$992$	−111.535	−	111.535i	−0.112434	−	0.112434i
$993$	300.581	−	300.581i	0.302700	−	0.302700i
$994$		−	105.435i		−	0.106071i
$995$	−341.925	−	900.286i	−0.343643	−	0.904810i
$996$	125.555			0.126059
$997$	−316.733	−	316.733i	−0.317686	−	0.317686i	0.530192	−	0.847878i	$-0.322120\pi$
$997$	−316.733	−	316.733i	−0.317686	−	0.317686i	−0.847878	+	0.530192i	$0.822120\pi$
$998$	−82.6128	+	82.6128i	−0.0827783	+	0.0827783i
$999$		−	44.4245i		−	0.0444690i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.3.f.a.7.2	✓	4
3.2	odd	2		45.3.g.b.37.1		4
4.3	odd	2		240.3.bg.a.97.2		4
5.2	odd	4		75.3.f.c.43.1		4
5.3	odd	4	inner	15.3.f.a.13.2	yes	4
5.4	even	2		75.3.f.c.7.1		4
8.3	odd	2		960.3.bg.h.577.1		4
8.5	even	2		960.3.bg.i.577.2		4
9.2	odd	6		405.3.l.f.352.1		8
9.4	even	3		405.3.l.h.217.1		8
9.5	odd	6		405.3.l.f.217.2		8
9.7	even	3		405.3.l.h.352.2		8
12.11	even	2		720.3.bh.k.577.2		4
15.2	even	4		225.3.g.a.118.2		4
15.8	even	4		45.3.g.b.28.1		4
15.14	odd	2		225.3.g.a.82.2		4
20.3	even	4		240.3.bg.a.193.2		4
20.7	even	4		1200.3.bg.k.193.1		4
20.19	odd	2		1200.3.bg.k.1057.1		4
40.3	even	4		960.3.bg.h.193.1		4
40.13	odd	4		960.3.bg.i.193.2		4
45.13	odd	12		405.3.l.h.298.2		8
45.23	even	12		405.3.l.f.298.1		8
45.38	even	12		405.3.l.f.28.2		8
45.43	odd	12		405.3.l.h.28.1		8
60.23	odd	4		720.3.bh.k.433.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.3.f.a.7.2	✓	4	1.1	even	1	trivial
15.3.f.a.13.2	yes	4	5.3	odd	4	inner
45.3.g.b.28.1		4	15.8	even	4
45.3.g.b.37.1		4	3.2	odd	2
75.3.f.c.7.1		4	5.4	even	2
75.3.f.c.43.1		4	5.2	odd	4
225.3.g.a.82.2		4	15.14	odd	2
225.3.g.a.118.2		4	15.2	even	4
240.3.bg.a.97.2		4	4.3	odd	2
240.3.bg.a.193.2		4	20.3	even	4
405.3.l.f.28.2		8	45.38	even	12
405.3.l.f.217.2		8	9.5	odd	6
405.3.l.f.298.1		8	45.23	even	12
405.3.l.f.352.1		8	9.2	odd	6
405.3.l.h.28.1		8	45.43	odd	12
405.3.l.h.217.1		8	9.4	even	3
405.3.l.h.298.2		8	45.13	odd	12
405.3.l.h.352.2		8	9.7	even	3
720.3.bh.k.433.2		4	60.23	odd	4
720.3.bh.k.577.2		4	12.11	even	2
960.3.bg.h.193.1		4	40.3	even	4
960.3.bg.h.577.1		4	8.3	odd	2
960.3.bg.i.193.2		4	40.13	odd	4
960.3.bg.i.577.2		4	8.5	even	2
1200.3.bg.k.193.1		4	20.7	even	4
1200.3.bg.k.1057.1		4	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	15.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.224745 + 0.224745i) q^{2} +(-1.22474 + 1.22474i) q^{3} -3.89898i q^{4} +(-4.67423 + 1.77526i) q^{5} -0.550510 q^{6} +(3.44949 + 3.44949i) q^{7} +(1.77526 - 1.77526i) q^{8} -3.00000i q^{9} +(-1.44949 - 0.651531i) q^{10} +11.3485 q^{11} +(4.77526 + 4.77526i) q^{12} +(-5.55051 + 5.55051i) q^{13} +1.55051i q^{14} +(3.55051 - 7.89898i) q^{15} -14.7980 q^{16} +(-17.3485 - 17.3485i) q^{17} +(0.674235 - 0.674235i) q^{18} +8.69694i q^{19} +(6.92168 + 18.2247i) q^{20} -8.44949 q^{21} +(2.55051 + 2.55051i) q^{22} +(11.5505 - 11.5505i) q^{23} +4.34847i q^{24} +(18.6969 - 16.5959i) q^{25} -2.49490 q^{26} +(3.67423 + 3.67423i) q^{27} +(13.4495 - 13.4495i) q^{28} +35.1464i q^{29} +(2.57321 - 0.977296i) q^{30} +10.6969 q^{31} +(-10.4268 - 10.4268i) q^{32} +(-13.8990 + 13.8990i) q^{33} -7.79796i q^{34} +(-22.2474 - 10.0000i) q^{35} -11.6969 q^{36} +(-6.04541 - 6.04541i) q^{37} +(-1.95459 + 1.95459i) q^{38} -13.5959i q^{39} +(-5.14643 + 11.4495i) q^{40} +0.696938 q^{41} +(-1.89898 - 1.89898i) q^{42} +(-26.4949 + 26.4949i) q^{43} -44.2474i q^{44} +(5.32577 + 14.0227i) q^{45} +5.19184 q^{46} +(44.2474 + 44.2474i) q^{47} +(18.1237 - 18.1237i) q^{48} -25.2020i q^{49} +(7.93189 + 0.472194i) q^{50} +42.4949 q^{51} +(21.6413 + 21.6413i) q^{52} +(-0.696938 + 0.696938i) q^{53} +1.65153i q^{54} +(-53.0454 + 20.1464i) q^{55} +12.2474 q^{56} +(-10.6515 - 10.6515i) q^{57} +(-7.89898 + 7.89898i) q^{58} -39.9342i q^{59} +(-30.7980 - 13.8434i) q^{60} +5.90918 q^{61} +(2.40408 + 2.40408i) q^{62} +(10.3485 - 10.3485i) q^{63} +54.5051i q^{64} +(16.0908 - 35.7980i) q^{65} -6.24745 q^{66} +(-45.1010 - 45.1010i) q^{67} +(-67.6413 + 67.6413i) q^{68} +28.2929i q^{69} +(-2.75255 - 7.24745i) q^{70} -68.0000 q^{71} +(-5.32577 - 5.32577i) q^{72} +(77.7878 - 77.7878i) q^{73} -2.71735i q^{74} +(-2.57321 + 43.2247i) q^{75} +33.9092 q^{76} +(39.1464 + 39.1464i) q^{77} +(3.05561 - 3.05561i) q^{78} -24.4949i q^{79} +(69.1691 - 26.2702i) q^{80} -9.00000 q^{81} +(0.156633 + 0.156633i) q^{82} +(13.1464 - 13.1464i) q^{83} +32.9444i q^{84} +(111.889 + 50.2929i) q^{85} -11.9092 q^{86} +(-43.0454 - 43.0454i) q^{87} +(20.1464 - 20.1464i) q^{88} +82.1816i q^{89} +(-1.95459 + 4.34847i) q^{90} -38.2929 q^{91} +(-45.0352 - 45.0352i) q^{92} +(-13.1010 + 13.1010i) q^{93} +19.8888i q^{94} +(-15.4393 - 40.6515i) q^{95} +25.5403 q^{96} +(-24.5959 - 24.5959i) q^{97} +(5.66403 - 5.66403i) q^{98} -34.0454i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 4 q^{5} - 12 q^{6} + 4 q^{7} + 12 q^{8} + 4 q^{10} + 16 q^{11} + 24 q^{12} - 32 q^{13} + 24 q^{15} - 20 q^{16} - 40 q^{17} - 12 q^{18} - 36 q^{20} - 24 q^{21} + 20 q^{22} + 56 q^{23} + 16 q^{25}+ \cdots - 188 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 - 4 * q^5 - 12 * q^6 + 4 * q^7 + 12 * q^8 + 4 * q^10 + 16 * q^11 + 24 * q^12 - 32 * q^13 + 24 * q^15 - 20 * q^16 - 40 * q^17 - 12 * q^18 - 36 * q^20 - 24 * q^21 + 20 * q^22 + 56 * q^23 + 16 * q^25 + 88 * q^26 + 44 * q^28 - 24 * q^30 - 16 * q^31 - 76 * q^32 - 36 * q^33 - 40 * q^35 + 12 * q^36 + 64 * q^37 - 96 * q^38 + 48 * q^40 - 56 * q^41 + 12 * q^42 - 8 * q^43 + 36 * q^45 - 136 * q^46 + 128 * q^47 + 48 * q^48 + 164 * q^50 + 72 * q^51 - 80 * q^52 + 56 * q^53 - 124 * q^55 - 72 * q^57 - 12 * q^58 - 84 * q^60 + 200 * q^61 + 88 * q^62 + 12 * q^63 - 112 * q^65 + 24 * q^66 - 200 * q^67 - 104 * q^68 - 60 * q^70 - 272 * q^71 - 36 * q^72 + 76 * q^73 + 24 * q^75 + 312 * q^76 + 88 * q^77 + 120 * q^78 + 164 * q^80 - 36 * q^81 + 128 * q^82 - 16 * q^83 + 232 * q^85 - 224 * q^86 - 84 * q^87 + 12 * q^88 - 96 * q^90 - 16 * q^91 + 104 * q^92 - 72 * q^93 + 144 * q^95 - 84 * q^96 - 20 * q^97 - 188 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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